The Texans chose Delhomme over Jeff Garcia after both quarterbacks worked out on Tuesday.
Delhomme is expected to be the third-string quarterback behind rookie T.J. Yates and Kellen Clemens, who was signed last week.
The 36-year-old Delhomme started four games for the Cleveland Browns in 2010 before giving way to then-rookie Colt McCoy. Delhomme has thrown for 20,764 yards with 125 touchdowns and 101 interceptions in 10 NFL seasons.
The Texans are currently two games ahead of the Tennessee Titans for first place in the AFC South, but are down to Yates at quarterback after Matt Schaub and Matt Leinart suffered season-ending injuries.
Schaub has already been placed on season-ending injured reserve because of a right foot injury, while Leinart suffered a fracture in his throwing shoulder in Sunday's game against Jacksonville.
Yates -- a fifth-round draft pick out of North Carolina -- came in for Leinart and led Houston to the 20-13 win.