The 22-year-old, who netted 20 times last season with Dagenham and then Darren Ferguson's Posh, has signed a four-year contract with the Premier League side.
Gayle's top flight move caps a memorable year for the forward who only turned professional with Dagenham 12 months ago after scoring 29 goals during a loan spell at Conference North outfit Bishop's Stortford.
"I'm ecstatic really, I just want to get pre-season started now," he told Palace's official website.
"The chance came and I had to grab it because I might not get another chance. To be playing in the Premier League from where I've come from is a big achievement really.
"I'm just really looking forward to it and hopefully I can take the opportunity with both hands and do well."
Gayle was playing in the Essex Senior League with Stansted until 2011.