Gayle, 25, has agreed a five-year deal for a reported £10million transfer fee to become manager Rafael Benitez's second summer signing. Andros Townsend has moved in the opposite direction for £13m.
"It's a dream come true to be at a big club like this," Gayle told the club's official website.
"Newcastle has a massive fanbase and a great history so it is amazing to be here.
"I can't wait to get started, prove myself and score the goals that take us back up to the Premier League. It's where this club belongs."
A deal for Gayle was agreed between the two clubs earlier this week and it is understood he completed his medical on Thursday.
Gayle scored 26 goals in 74 appearances in all competitions for Palace since arriving at Selhurst Park in a £4.5million deal from Sky Bet League 1 side Peterborough in July 2013.
He began his professional career at Dagenham and had a loan spell at Bishop's Stortford and joined Peterborough in January 2013 following a temporary stint with the club.
Gayle was an instant hit with Posh, scoring 13 goals in 29 appearances and six months later he moved on to Palace, where he finished top goalscorer in each of his three seasons.
Benitez added: "Dwight is a great player, a proven goalscorer, and it is fantastic news that he has joined us.
"He has a big personality, a lot of energy and pace. He is a good finisher also, so he will add goals to our squad, for sure.
"He knows English football well, too, and that is important in the Championship.
"I am sure Dwight will want to prove he can make a big difference to our team and I am looking forward to working with him."
Newcastle signed goalkeeper Matz Sels from Belgian side Gent for an undisclosed fee on Wednesday.
Sels, 24, has signed a five-year contract after the two clubs agreed a reported fee of around £4.5million.
Newcastle are also understood to have met the reported £10million asking price for Bournemouth winger Matt Ritchie.