Lawrie's deal is for $4,125,000, more than double his $1,925,000 salary last season with Oakland. Jennings gets $810,000.
The agreements were announced Thursday.
Acquired from the Athletics in December, Lawrie set career bests in virtually every category last season - his first with the A's. He batted .260 with 16 home runs, 60 RBIs and 64 runs. He made 106 starts at third base and 40 at second.
Jennings went 2-3 with a 3.99 ERA in 53 appearances for Chicago last season, when his salary was $523,000.