Wood was last with the Patriots on their practice squad, but didn't stick with New England and was released Dec. 26 after being signed Nov. 5.
Wood was cut by the Texans in October along with defensive end Sam Montgomery and outside linebacker Willie Jefferson for violating team rules. They were allegedly smoking marijuana the night before a game against the Kansas City Chiefs, according to reports.
Wood and the other players have denied using marijuana through their agents, saying they were merely smoking a regular cigar.
Wood visited the Jacksonville Jaguars prior to signing with New England.
Wood rushed for nine yards on three carries in three games with the Texans this season.
The 5-foot-11, 215-pound rookie played collegiately at Notre Dame.
He ran the 40-yard dash in 4.46 seconds at the NFL scouting combine last year.
After serving a two-game suspension as a senior for violating team rules, Wood rushed for 742 yards and four touchdowns.
As a junior, he rushed for 1,102 yards and nine touchdowns and caught 27 passes for 187 yards.