The 6-foot-6, 310-pound interior lineman made four starts and played in 11 games with Indianapolis last season. He also spent five weeks on the Los Angeles Rams' practice squad.
He became a restricted free agent in March and is the 11th free agent re-signed by the Colts. Only one player, receiver Ryan Grant, has left for a new team. Grant signed with Oakland.
Boehm spent his first two seasons with the Arizona Cardinals, has played in 42 games during his career and helped the Cols allow a league-low 18 sacks in 2018.
Indy has the 26th overall selection in this week's draft.