Coleman started all 16 games at right tackle for the Browns in 2017. He began last season competing to replace the retired Joe Thomas at left tackle but wound up on the right side and eventually on the second unit.
The 6-foot-5, 310-pound Coleman must pass a physical with the 49ers for the deal to be finalized.
The 49ers are likely to use Coleman for depth on the offensive line. They have Joe Staley set to start at left tackle and rookie Mike McGlinchey, a first-round draft pick this year, on the right side.
The 26-year-old Coleman played in 32 games and started 25 in five years at Auburn. He was named second-team All-SEC as a senior in 2015.
The 49ers also cut 12 players on Friday: offensive linemen JP Flynn and Darrell Williams, running backs Ja'Quan Gardner and Joe Williams, guard Chris Gonzalez, quarterback Jack Heneghan, defensive lineman Chris Jones, punter Jeff Locke, offensive tackle Pace Murphy, wide receiver Aldrick Robinson, tight end Wes Saxton and defensive lineman Will Sutton.
Rosters must be trimmed to 53 players by 4 p.m. ET Saturday.