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The 19-year-old will join the academy set up in east London after nine years with the Royals.
The forward has nine goals in 25 Premier League 2 appearances at youth level, including a goal against his new club last year.
Nevers has agreed a three-year deal for a nominal fee which includes the option of a fourth year.
“I’m very excited to join West Ham United,” said Nevers.
“This move is probably the biggest step in my career so far. I feel very excited to see what the future holds – there’s a lot of opportunity here.
“It’s exciting to make that jump to a big Premier League club with a good historical foundation. The first team are doing well, and the academy have got a good reputation with the players they’ve brought through.
“I’m looking forward to hopefully hitting the ground running when I come back for pre-season, and then it all starts from there, from my very first day.”