The Colombia international has agreed terms with the Eagles to move to Selhurst Park on a three-year contract.
Lerma joined Bournemouth for a club record £25m fee from Levante in the summer of 2018 and made 183 appearances in total for the Cherries.
Lerma scored five times in 37 Premier League appearances this season as Bournemouth finished in 15th position.
'I am very happy and excited by this new opportunity,' Lerma told the official Palace website.
'Crystal Palace has good players and a good team, and I want to help with every objective the club has next season.'
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.'
Lerma has won 33 caps for the Colombia national team.
