The deal is worth $66 million with $50 million guaranteed, making Tunsil the highest-paid offensive lineman in the NFL, a source confirmed to ESPN's Adam Schefter.
Tunsil, 25, negotiated his extension without using an agent. Terms of the deal were first reported by the Houston Chronicle.
Tunsil was drafted by the Miami Dolphins in 2016 with the No. 13 pick. Texans head coach and general manager Bill O'Brien traded for him just before the start of the 2019 season for a package of draft picks, including two first-round selections.
In his first season in Houston, Tunsil helped the Texans' revamped offensive line go from allowing an NFL-high 68 sacks in 2018 to 49 sacks (ranked 25th in the league) in 2019. He was named to his first Pro Bowl, becoming the first Texans offensive lineman to make the team since left tackle Duane Brown in 2014.
However, Tunsil led the league with 17 penalties in 2019, including 14 false starts. He also had three penalties declined. In his final season with the Dolphins, Tunsil had only eight penalties.
At the end of last season, O'Brien said the Texans wanted to keep Tunsil in Houston.
"Look, we want Laremy here," O'Brien said in January. "Laremy knows that. ... I can unequivocally state to you that we want Laremy here for a long time."