Both players previously worked out for the team, as Wood was in Foxborough on Monday and Williams worked out on Oct. 15.
Williams, originally an undrafted free agent out of Maryland in 2011, was previously a member of the Ravens organization. Though not a big part of the Ravens' offense last season, he did bring special-teams value to their Super Bowl team.
Wood was undrafted out of Notre Dame this year but made the Texans' roster as a depth level running back. He was recently released after violating team rules during a trip for a road game in Kansas City. He played in three games for the Texans, rushing three times for a total of nine yards.
While the Patriots had an open spot on the practice squad, they will have to create an open active roster spot for Williams.