In Fifa, special players can be bought in packs, but the contents are only revealed after payment is completed.
The children's father, Thomas Carter, had bought them a single pack for around £8, and had not realised they had seen how he made the purchase.
The Switch has now been confiscated "indefinitely", Mr Carter said.
Nintendo has agreed to a full refund and has removed the purchased players.
While Fifa is published and sold by Electronic Arts, the payments had been made via the family's Nintendo account.
Nintendo did not respond to a request for comment.
Mr Carter, from Hampshire, admits that he did not take full precautions to limit access to his Nintendo account: he did not use a unique Pin number and the emailed receipts were sent to an old email address with a full inbox.
"I just never thought [the children] would do it," he said.
He and his wife only realised what had happened when their card was declined elsewhere because their bank account was empty.
Fifa 19 has been certified as suitable for players from the age of three.
Mr Carter said his children, who are all under the age of 10, felt very remorseful and had not understood the impact of what they were doing.
However, he also said he felt that the in-game concept of buying player packs without knowing what was inside them was unethical.
"You pay £40 (USD$49) for the game, which is a lot of money in itself, but then the only way to get a great team is essentially by gambling," he said, referring to online play.
"They spent £550 (USD$685) and they still never got their favourite player, Lionel Messi."
Video games publisher EA, which owns Fifa, declined to comment but provided a link to its guidelines on controlling in-game purchases - this varies depending on the platform or console being used.