Joseph, 35, has spent the past nine seasons with the Texans. He had 51 tackles, 13 pass breakups and one interception in 14 games last season.
"Johnathan has been a consummate professional, team captain and one of the leaders of our defense for the past nine years. It is rare for a player to sustain such a high level of play for over a decade and that says so much about him and his dedication to the game," the Texans said in a statement.
"He is an exceptional teammate, mentor, husband and father. His impact on and off the field makes him quite possibly the most celebrated free agent signing in franchise history. The entire Houston Texans organization thanks Johnathan for the contributions he made to our team and the Houston community. We wish him and his family all the best as he pursues free agency."
In 2019, Joseph played fewer than 60% of Houston's snaps -- the lowest percentage of his career -- because starting Week 13, he did not play consistently. In 2018, he played more than 75% of the team's snaps.
After the Texans lost to the Kansas City Chiefs in the divisional round of the playoffs, Joseph said he's not thinking about retirement.
Joseph has been selected to two Pro Bowls in 14 NFL seasons and has 31 interceptions, 195 passes defensed, 7 forced fumbles and 754 tackles in his career.
The Cincinnati Bengals drafted Joseph in 2006, and he played for them for five seasons.
ESPN's Sarah Barshop contributed to this report.