The Titans announced the deals Monday.
General manager Ruston Webster says both players are established veterans with plenty of starting experience who can help add to competition with the Titans.
Walter has started 93 of his 152 NFL games in his 10 seasons, and he spent the past seven years with the Titans' AFC South rival Houston. He had 41 catches for 518 yards and two touchdowns last season.
Spencer is an eight-year veteran with 89 starts in his 105 games played. He has started 62 games at center, 19 at right guard and eight at left guard while spending the past two seasons with the Chicago Bears.