The wideout has spent the last seven years with the Houston Texans, while Spencer comes from a two-year stint at the Chicago Bears.
General manager Ruston Webster said in a statement: "Both Kevin and Chris are established veterans in this league who have a great deal of starting experience.
"They have made significant contributions on good teams during their careers. We feel like they can come in and provide increased competition at their respective positions for us."
The Titans finished the 2012 season with six wins and 10 losses.