Per NFL Network's Ian Rapoport, Richburg's contract includes $16.5 million fully guaranteed and is worth up to $47.5 million.
A concussion limited Richburg to four games with the New York Giants last season. The 26-year-old had a streak of 25 consecutive games started at center from 2015-17.
Richburg played at left guard during his rookie season in 2014 before moving to center. He was ranked as the fourth-best center in the NFL last season before getting hurt, according to Pro Football Focus.
The team previously announced a three-year extension with Daniel Kilgore, who started all 16 games at center in 2017. He also has experience at left guard in his career.
The addition of Richburg gives 49ers head coach Kyle Shanahan more versatility and depth on the offensive line to protect quarterback Jimmy Garoppolo.