Wilfork will sign a two-year deal worth $9 million, including $5 million in guaranteed money, a league source told ESPN NFL Insider Adam Schefter.
The 33-year-old said he wanted to turn the Texans, who have missed the playoffs the past two seasons after winning back-to-back division titles in 2011 and 2012, into a contender again.
"My goal is to help this team win as many games as possible and bring winning to this town," he said. "I think we deserve that, so that's my No. 1 goal."
Wilfork tweeted his decision to join the Texans and also posted a screenshot of a lengthier message in which he thanked the Patriots.
Wilfork became a free agent when the Patriots decided not to exercise his option for the 2015 season. The Patriots created $8.06 million in salary-cap space with the move.
He highlighted his past experience with the Texans' coaching staff, including Romeo Crennel, Mike Vrabel and Bill O'Brien, and he said he looked forward to working with franchise star J.J. Watt and up-and-comers Jadeveon Clowney, Brian Cushing and Johnathan Joseph.
"It's a young, exciting team to be around," Wilfork said. "My goal is just to bring leadership, bring a lot of fun and bring a lot of experience. I'm not a coach by no means, but at the same time, I've been on another level where I've won a lot of games and won Super Bowls. If guys want to know what it takes or how it feels, I'm here for that."
He likely will compete for a starting job with the Texans, who have a shortage on the interior of their defensive line.
Ryan Pickett started 13 games at nose tackle -- Wilfork's customary position -- in Houston's 3-4 defensive scheme last season. But the 35-year-old Pickett was not re-signed this offseason and may consider retirement.
Houston also has second-year defensive lineman Louis Nix III, who underwent knee surgery before last season and did not appear in a game as a rookie.
Wilfork returned from a torn Achilles tendon in 2014 and played 73.4 percent of New England's defensive snaps. His primary responsibility was to take on multiple blockers against the run and provide a powerful pocket-pushing presence up the middle on passing plays.
A five-time Pro Bowler, Wilfork won two Super Bowls in his 11 seasons with the Patriots. In thanking the Patriots, he praised New England coach Bill Belichick, saying he has been "very blessed and privileged to play up there and learn from the best coach that ever done it."
The normally stoic Belichick was just as effusive in his praise of the former Patriot.
"Few players reached or will ever reach the special level of Vince Wilfork. He is a great champion and one of the classiest people I have ever been around -- just a kind, genuine and giving person who was all about our team, football, winning and bringing joy to others," Belichick said in a statement. "There may have never been anyone at his position with as much strength, toughness, intelligence, instinctiveness and athleticism.
"He is the best defensive lineman I ever coached, an all-time great Patriot whose place on our team will be missed but whose remarkable career as a Patriot will be remembered forever."
ESPN.com Patriots reporter Mike Reiss and Texans reporter Tania Ganguli contributed to this report.