The deal includes $8.5 million in guaranteed money, the source said.
Taylor, who turned 32 last August, joined the Texans last offseason on a one-year deal worth up to $12.5 million and became the starter with Deshaun Watson not playing for the team after he requested a trade and because of 22 lawsuits filed against him alleging sexual assault or sexually inappropriate behavior during massage sessions.
After a strong Week 1 performance, Taylor injured his left hamstring in Week 2. He missed six games on injured reserve before returning in a Week 9 loss to the Miami Dolphins. Taylor struggled in his return, throwing five interceptions and taking 12 sacks in four games. He was benched in Week 13 against the Indianapolis Colts for rookie quarterback Davis Mills, who finished the season as the starter.
For the season, Taylor completed 60.7% of his passes for 966 yards, 5 touchdowns and 5 interceptions.
Before joining Houston, Taylor signed a two-year deal with the Los Angeles Chargers in 2019 and, after playing behind Philip Rivers his first season, was named the starter in 2020. That, however, lasted just one game because a team doctor accidentally punctured his lung with a pain-killing shot while attempting to treat a rib injury before a Week 2 game. When he was healthy enough to return, Taylor remained on the bench as the backup to rookie starter Justin Herbert.
In 78 career games, including 53 starts, Taylor has completed 61.3% of his passes for 10,736 yards, with 59 touchdowns and 25 interceptions.
ESPN’s Sarah Barshop contributed to this report.