Jackson's contract is worth $34 million with $20 million in guarantees, NFL Network's Ian Rapoport reported.
Jackson wrote a pair of tweets that appeared to confirm his signing.
Jackson, 27 next month, spent the first five seasons of his career with the Texans. In 13 games last season, Jackson intercepted three passes, deflected nine and recorded 57 tackles.
[daily_cut.nfl]Over his career, he has 10 interceptions, 50 pass deflections and 279 tackles.
NFL.com ranked Jackson No. 23 on its list of 2015 free agents.
After the Texans drafted Jackson 20th overall in 2010, he signed a five-year, $13.1 million contract. Houston's other starting cornerback opposite Jackson, Jonathan Joseph, is set to make $8.5 million next season with a $12.2 million cap hit, third-highest on the team. According to the Houston Chronicle, the Texans will have $27.3 million in cap space after wide receiver Andre Johnsonis traded or released.
Teams and free agents were allowed to begin negotiating on Saturday, but contracts cannot be signed until free agency begins Tuesday afternoon.
Houston's passing defense ranked 21st last season (243.1 yards allowed per game) and its total defense ranked 16th (348.2).
- Mike Fiammetta