James (e, por extensão, Harry) ficou rico da maneira antiga: ele tinha ancestrais ricos.

As sementes da fortuna de Potter foram colocadas pelo primeiro membro da família, Linfred de Stinchcombe, que inventou poções medicinais:

Linfred was a vague and absent-minded fellow whose Muggle neighbours often called upon his medicinal services. None of them realised that Linfred’s wonderful cures for pox and ague were magical; they all thought him a harmless and lovable old chap, pottering about in his garden with all his funny plants. His reputation as a well-meaning eccentric served Linfred well, for behind closed doors he was able to continue the series of experiments that laid the foundation of the Potter family’s fortune. Historians credit Linfred as the originator of a number of remedies that evolved into potions still used to this day, including Skele-gro and Pepperup Potion. His sales of such cures to fellow witches and wizards enabled him to leave a significant pile of gold to each of his seven children upon his death.

A Linfred estabeleceu as bases para as futuras gerações, embora as especificidades de cada geração não sejam registradas nesta história:

The Potters continued to marry their neighbours, occasionally Muggles, and to live in the West of England, for several generations, each one adding to the family coffers by their hard work and, it must be said, by the quiet brand of ingenuity that had characterised their forebear, Linfred.

A fortuna da família foi então expandida pelo avô de Harry, Fleamont Potter, que inventou a Poção de Cabelo de Sleekeazy:

It was Fleamont who took the family gold and quadrupled it, by creating magical Sleekeazy’s Hair Potion ( 'two drops tames even the most bothersome barnet' ). He sold the company at a vast profit when he retired, but no amount of riches could compensate him or his wife Euphemia for their childlessness.

¹ conta Pottermore não é necessária

O dinheiro de Harry veio da herança de seu pai, James.

James era rico (com dinheiro da família) quando saiu de Hogwarts, o suficiente para se sustentar, Sirius e Lily como combatentes em tempo integral (não-remunerados) da Ordem da Fênix. Além disso, não há informações de onde veio a riqueza de James ou o que seus pais (os avós paternos de Harry) faziam para ganhar a vida ou como ganhavam dinheiro.

Fonte: Entrevista da JKR por um jovem de 14 anos garoto chamado Owen Jones, que ganhou a chance em 2005 para entrevistá-la.

Q: Where does he [Harry] get his money? He always seems to have some. Does he have a bank account? Where is it? Where's his money?

JKR: Well, as you know, Harry's bank account is in Gringotts. His money came from inheritance, from his father. But I think, on a deeper level... [On the one hand,] Harry's money never really is that important in the books, except that he can afford his uniform and so on. [On the other hand,] I think I really gave him a fortune because I was so broke when I wrote the first book and it was wishful thinking that I would not have to worry about such things.

De uma entrevista anterior, de J.K.Rowling:

Q: What did James and Lily Potter do when they were alive?

JKR: Well, I can't go into too much detail, because you're going to find out in future books. But James inherited plenty of money, so he didn't need a well-paid profession. You'll find out more about both Harry's parents later.

Não está muito claro quanto ainda resta, porque James precisava apoiar Lupin também:

Jo related the fact that Remus Lupin, prior to the third book, was unemployable because he was a werewolf, and upon his graduation from Hogwarts, along with James and Lily, was supported by James using their own money. In addition to this, she shed more light on the early days of the Order, saying James, Sirius, Remus and Lily were full time Order members. "Full Time Fighters," as Jo put it.
- J. K. Rowling at Carnegie Hall, 2007

Nunca é realmente explicado de onde vem o dinheiro que resta para Harry. Seus avós em ambos os lados aparentemente estão mortos antes do início do primeiro livro, possivelmente nas mãos dos Comensais da Morte.

Dizem no livro e no filme do Hagrid: "você realmente não acha que seus pais deixariam você com nada?" Novamente, não está claro o que James e Lily faziam para ganhar a vida, se eles tivessem que trabalhar para ganhar a vida (talvez James fosse de fato independente rico; ele é tão convencido quando criança para ser herdeiro), mas se eles funcionassem, eles provavelmente teriam algum tipo de fundo de aposentadoria para o qual eles tinham sido empurrados, o que passaria a Harry como parente mais próximo.

ykombinator está correto, pois Harry herdou seu dinheiro do lado do pai da família. Novas informações do J.K. Rowling, lançado em Pottermore , no entanto, entra em mais detalhes sobre a fonte da fortuna dos oleiros.

The wizarding family of Potters descends from the twelfth-century wizard Linfred of Stinchcombe, a locally well-beloved and eccentric man, whose nickname, ‘the Potterer’, became corrupted in time to ‘Potter’. Linfred was a vague and absent-minded fellow whose Muggle neighbours often called upon his medicinal services. None of them realised that Linfred’s wonderful cures for pox and ague were magical; they all thought him a harmless and lovable old chap, pottering about in his garden with all his funny plants. His reputation as a well-meaning eccentric served Linfred well, for behind closed doors [Linfred] was able to continue the series of experiments that laid the foundation of the Potter family’s fortune. Historians credit Linfred as the originator of a number of remedies that evolved into potions still used to this day, including Skele-gro and Pepperup Potion. His sales of such cures to fellow witches and wizards enabled him to leave a significant pile of gold to each of his seven children upon his death.

Além disso, foi um Potter que inventou o Sleekeazy Potion, o tônico que Hermione usa para controlar seu cabelo selvagem e peludo no Baile de Inverno em Cálice de Fogo :

It was Fleamont [Potter] who took the family gold and quadrupled it, by creating magical Sleekeazy’s Hair Potion ( ‘two drops tames even the most bothersome barnet’ ). He sold the company at a vast profit when he retired, but no amount of riches could compensate him or his wife Euphemia for their childlessness. They had quite given up hope of a son or daughter when, to their shock and surprise, Euphemia found that she was pregnant and their beloved boy, James, was born.

James herdou essa fortuna de acordo, e quando ele e Lily foram mortos, a fortuna de Harry Potter passou para Harry.

Harry é um descendente dos Peverells, uma família antiga e magicamente poderosa (e, portanto, potencialmente rica, como os Malfoys). Ele herdou o manto da invisibilidade que pertencia a Ignoto, então, presumivelmente, qualquer fortuna familiar também teria sido passada de pai para filho.

Nos rascunhos originais de Rowling, eles fizeram fortuna com a Pedra Filosofal,

(eles podem ou não ter roubado isso dos Flamels.)

“But he's dead now?” he [Ron] asked.
“Of course,” said Harry, “Someone stole his stone so he couldn't make any more Elixir of life, could he? It takes a while to make another stone and by that time, I suppose, he was just too old to live without his Elixir until a new stone was ready. “And now I’ll tell you something else really weird that I haven't told you up to now— the stone was found in my parents safe at Gringott’s bank.”
But instead of the interested noises Harry had expected, Ron and Hermione simply stared at him.
_{(The old jkrowling.com - Scrapbook entry #1 - "Very early page of Philosopher's Stone")}

No cânone final, como outros apontaram, eles fizeram fortuna com a venda de produtos para os cabelos.

It was Fleamont who took the family gold and quadrupled it, by creating magical Sleekeazy’s Hair Potion (‘two drops tames even the most bothersome barnet’).
_{(Pottermore: The Potter Family)}

Eu deixo você decidir qual versão soa melhor.

De Harry Potter e as Relíquias da Morte, Capítulo 21 - O Conto dos Três Irmãos

"Ah, but the Third Hallow is a true Cloak of Invisibility, Miss Granger!"

...

"Exactly," said Xenophilius, as if he had defeated them all in reasoned argument. "None of you have ever seen such a thing. The possessor would be immeasurably rich, would he not?"

Para uma resposta anterior de alguém sobre como ele não comprou sua Firebolt, a única razão que ele não fez foi que ele não queria desperdiçar uma grande parte do dinheiro que ele precisaria para passar mais cinco anos em Hogwarts. .

Sirius comprou a Harry a Firebolt como presente para compensar os 13 aniversários que faltavam. Também tinha um significado mais significativo por trás disso porque, no primeiro aniversário de Harry, Sirius havia comprado para ele uma pequena vassoura de brinquedo para crianças bruxas passarem.

Mas tanto os Potters quanto os Blacks eram puros-sangues extremamente ricos e, como James era filho único, ele herdou tudo. Como Sirius era a única criança viva no momento da morte de sua mãe, ele a herdou por sua vez. Então, quando Harry finalmente herdou o dinheiro e os bens de ambas as famílias, ele foi considerado extremamente rico pelos padrões dos bruxos; provavelmente perto, se não mais do que, dos Malfoys.

Também é possível que parte do dinheiro venha de recompensas por capturar Comensais da Morte durante a primeira guerra com Voldemort.

The Dursleys couldn't have known about this or they'd have had it from him faster than blinking.

De Pottermore :

The wizarding family of Potters descends from the twelfth-century wizard Linfred of Stinchcombe, a locally well-beloved and eccentric man, whose nickname, ‘the Potterer’, became corrupted in time to ‘Potter’. Linfred was a vague and absent-minded fellow whose Muggle neighbours often called upon his medicinal services. None of them realised that Linfred’s wonderful cures for pox and ague were magical; they all thought him a harmless and lovable old chap, pottering about in his garden with all his funny plants. His reputation as a well-meaning eccentric served Linfred well, for behind closed doors he was able to continue the series of experiments that laid the foundation of the Potter family’s fortune. Historians credit Linfred as the originator of a number of remedies that evolved into potions still used to this day, including Skele-gro and Pepperup Potion. His sales of such cures to fellow witches and wizards enabled him to leave a significant pile of gold to each of his seven children upon his death.

Mais adiante no artigo:

The Potters continued to marry their neighbours, occasionally Muggles, and to live in the West of England, for several generations, each one adding to the family coffers by their hard work.

E ...

...Fleamont Potter... It was Fleamont who took the family gold and quadrupled it, by creating magical Sleekeazy’s Hair Potion ( ‘two drops tames even the most bothersome barnet’ ). He sold the company at a vast profit when he retired.

Fleamont Potter era o pai de James Potter.