The 26-year-old Schwartz, a second-round pick in 2012, has been consistent and dependable -- playing in 4,427 of the 4,427 offensive snaps since he came to Cleveland.
Also Wednesday, the Browns lost center Alex Mack to Atlanta, where he signed a five-year deal with the Falcons.
Schwartz is a cerebral player dubbed "the Oracle" by his fellow linemen, "because he's so smart he knows everything," teammate Joe Thomas has said.
According to ProFootballFocus, the Broncos' Von Miller had only one game when he had a negative grade -- when he lined up across from Schwartz in Week 6 last season.
The analytics site rated Schwartz as one of the top two or three best tackles in the league, crediting him with allowing just three sacks, eight hits and 32 hurries in 705 pass-rush snaps. The 705 pass-blocking snaps tied for the most in the league -- and Browns quarterbacks held the ball longer than the league average.
ESPN Browns reporter Pat McManamon contributed to this report.