The defensive tackle from Texas was the 81st overall selection in the draft. His signing Monday leaves the Bucs with one unsigned pick, first-rounder Josh Freeman.
To make room on the roster for Miller, backup quarterback Brian Griese, who started five games last season, was released. The 34-year-old has thrown for 19,440 yards, 119 touchdowns and 99 interceptions in 11 seasons with Denver, Miami, Chicago and Tampa Bay.
Miller started 19 of 49 games he appeared in at Texas, finishing his career for the Longhorns with 138 tackles and 10 sacks.