The second season of the deal contains a player option.
Harrell won the league's 2019-20 Sixth Man of the Year award while playing for the Los Angeles Clippers, the Lakers' in-arena rival.
The 26-year-old becomes Lakers vice president of basketball operations Rob Pelinka's latest high-profile acquisition this offseason. The team recently acquired Dennis Schroder - another player who was in the mix for Sixth Man of the Year honors with Harrell - and reportedly signed Wesley Matthews.
Harrell's stunning departure appears to have irked former teammate Patrick Beverley, who initially expressed his disapproval of the move on social media.
The Clippers guard later congratulated the big man on the signing.
Harrell averaged 18.6 points and 7.1 rebounds while shooting 58% from the field in 63 games last season.