The Eagles had hoped to bring in the 31-year-old during the January transfer window, with a medical rumoured to have been passed, only for Getafe to stand firm.
After biding their time, Palace will now land the Spanish keeper on a free contract on July 1, providing competition for Wayne Hennessey in goal next season.
Guaita, who kept 12 clean sheets last term to help Getafe to an eighth-place finish in La Liga, has been handed a three-year deal at Selhurst Park.
Palace chairman Steve Parish told the club's official website: "We are delighted to sign one of La Liga's best goalkeepers and pleased that we beat off the competition for his signature.
"We very much look forward to Vicente joining in pre-season training and helping us push on in the Premier League."
Guaita is Palace boss Roy Hodgson's first signing of the summer transfer window.