The team didn't announce terms of the contract but a league source told ESPN NFL Insider Adam Schefter it's a one-year deal.
Walton underwent surgery on Monday, the team confirmed Wednesday, with a story on the team's website saying he is expected to be sidelined until the middle of October.
According to The Denver Post, which had reported Walton's surgery earlier Wednesday, Walton could miss the entire 2013 season if he suffers any complications in his rehab from the surgery, which was done to replace hardware inserted into his ankle during a surgery to repair an injury he suffered last year.
Walton's season ended on Oct. 1 last season when the Broncos placed him on injured reserve with a broken and dislocated left ankle. Koppen replaced Walton in the starting lineup last season.
Koppen, 33, was released by the New England Patriots before last season after 10 seasons with the team. He started 12 games for the Broncos after signing with the team.
Manny Ramirez has worked at center for the Broncos this offseason.
ESPN NFL Insider Adam Schefter contributed to this report.