The club disclosed the move on Twitter.
Smelley, who can also play fullback, signed with the Texans’ practice squad on Dec. 3. A seventh-round pick of the Browns in 2012, Smelley appeared in two regular-season games for Cleveland as a rookie. He played collegiately at Alabama.
Smelley figures to be the Texans’ third-string tight end behind Garrett Graham and Ryan Griffin.
Byrne, a first-year pro from Wisconsin, had been on the Texans’ roster since Oct. 9. He played in seven games for Houston.