The midfielder spent five seasons with the Cherries after joining for a club-record fee in 2018, making 184 appearances, and he was named Bournemouth’s Player of the Year last month after another impressive campaign.
“Jefferson is a strong addition to our squad,” Palace chairman Parish told the club’s official website.
“He is a proven performer at Premier League level, and his combative and competitive nature will endear him to the Palace fans. We look forward to welcoming him to the club on 1st July in preparation for our eleventh consecutive season in the top-flight.”
Lerma said: “I am very happy and excited by this new opportunity. Crystal Palace has good players and a good team, and I want to help with every objective the club has next season.”