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 newly promoted Barclays 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, www.cpfc.co.uk.
"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.
Eagles manager Ian Holloway added on the club website: "I'm absolutely delighted. I was very annoyed when we didn't get him last year, to be honest.
"But now it makes a huge statement for us and it proves that I don't care where I get my people from. I believe it's about how good you're going to be, not just how good you are already.
"I think this fella has got Crystal Palace stamped all over him - the way he moves, the way he chases, the way he works. He's hungry for success and I'm absolutely thrilled that after long conversations we've come up with, I think, a proper Palace player.
"He's got an opportunity now to go and enjoy his football and I think he'll score goals at Premier League level, I really do. He's born to score goals."