Gayle joined the Eagles this week from Peterborough United in a multi-million pound deal - despite starting last year playing for Bishop's Stortford in the Conference North.
"I can't believe what's happened," Gayle told Sky Sports News. "It's so exciting to be playing in the Premier League next season.
"I just can't wait for it to get started and get a few games under my belt. It's just a dream come true really.
"If you'd told me a year ago I could be walking out at Old Trafford, it is unbelievable.
"I'm most excited about playing against big players, seeing what I can achieve and playing against Manchester United."
It's been a remarkable rise but the 22-year-old is backing himself to cope with the added attention.
"I'm going to handle it because I think the people around me will keep my feet on the ground," he added
"It's difficult to deal with all the attention I've been getting but I should be fine."
Palace boss Ian Holloway has shown real faith in the youngster and the player himself is impressed by what he has seen from his new manager.
"After speaking to him, I think we are going to get on just fine," said Gayle. "He's down to earth and seems pretty straightforward.
"He seems like a good coach and what he's achieved is very good so I can't wait to work with him."