Media reports said the final fee could reach 8.5 million pounds for the 22-year-old who was signed from League 1 Peterborough United after a career spent largely in the lower reaches of English football.
"The chance came and I just had to grab it because I might not get another," Gayle told the Palace website.
"I'm ecstatic really. To be playing in the Premier League from where I've come from is a big achievement."
A former Arsenal youth player, Gayle played minor league football before signing for League 2 Dagenham & Redbridge as a trainee.
He turned professional a year ago and moved to Peterborough on loan before signing for them in January this year.
"It's a huge statement from us and it proves that I don't care where I get my people from," said Palace manager Ian Holloway. "I believe it's about how good you're going to be, not just how good you are already.
"I think this fellow 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."
Gayle once scored 57 goals in a campaign in minor league football and last season netted 13 times in 29 games for Peterborough including a hat-trick in 27 minutes against Blackburn Rovers in March.
Peterborough were relegated from the Championship at the end of last season.
"He'll score goals at Premier League level. He's born to score goals," said Holloway. "Goals from certain people just keep happening, it doesn't matter which level you start at, they just keep happening.
"The boy moves like a top player. My chairman [Steve Parish] went in with a brief - don't come out of the room without getting him - and I'm thankful. He's given us a goal scorer of the future in our team right now which is priceless."
