The 6-6, 309-pound Painter is likely to compete for a backup role on the Denver offensive line.
Painter, 23, started 13 games at right tackle for Virginia Tech in 2012. He also got looks at guard and defensive tackle earlier in his career. He was a reserve before entering the starting lineup last year.
Painter is the first member of the club’s six-player draft class to sign a contract, the club said.