Winston, 30, will compete with Michael Bowie and rookie Justin Britt at the right tackle position.
While Bowie was sidelined with a shoulder injury at practice Monday, Britt took reps with the first team. The team continues to search for a mainstay on the right side as it allowed Breno Giacomini to sign a deal with the New York Jets during free agency.
After struggling in Arizona last season, Winston had spent much of the offseason training with former Texans teammates running back Arian Foster and wide receiver Andre Johnson in Houston.
"He looks phenomenal," one source close to Winston told FOXSports.com. "Body looks and feels healthy. He’s just been preparing and staying ready for a team."
Health, however, has never been a factor for Winston as he has started 119 games in eight seasons.