Bournemouth recently confirmed that the Colombia international will leave the club when his contract runs out at the end of June.
Lerma joined the Cherries from Levante for a club-record £25m fee in the summer of 2018, and he went on to make 184 appearances for the club, scoring 12 goals and eight assists.
The midfielder featured regular for the South Coast side during the 2022-23 season, starting 37 of the club's 38 Premier League games.
Despite leaving Bournemouth, Lerma will remain the Premier League after agreeing a three-year contract with Palace.
Speaking to the club's official website, 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."
Lerma will strengthen a Palace midfield that has been weakened by the departures of Luka Milivojevic and James McArthur.
The 28-year-old has a wealth of Premier League experience after making 100 top-flight appearances during his time with the Cherries.
Commenting on Lerma's imminent arrival, Palace chairman Steve Parish said: "Jefferson is a strong addition to our squad.
"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 1 July in preparation for our 11th consecutive season in the top flight."
Palace are yet to decide on a new permanent manager, with Roy Hodgson set to depart when his short-term contract comes to an end.
Hodgson returned to the Palace dugout in March, overseeing five wins in nine matches to guide the Eagles to an 11th-place finish.