Agent CJ LaBoy tweeted congratulations to Addae:
Last season, the Texans ranked 28th in the NFL in pass defense, allowing an average of 260 passing yards per game.
The hard-hitting Addae, who struggled with a move from strong safety to free safety in 2018, was released by the Los Angeles Chargers on March 9.
Signed as an undrafted rookie by the Chargers in 2013, Addae carved out a role as a special-teams standout and eventually earned a starting job as a strong safety in 2015. The team, however, moved him to free safety after drafting Derwin James before last season.
The move did not totally fit his skill set, and he finished the season with 75 combined tackles, a sack and an interception in 16 games.
Addae signed a four-year, $22 million contract two years ago and had $11.5 million in non-guaranteed compensation left on his deal when he was released.
In six seasons with the Chargers, Addae recorded 372 combined tackles, 21 pass breakups, 4.5 sacks and two interceptions.
ESPN's Eric D. Williams contributed to this report.