The deal is worth $80 million, a source told ESPN's Adam Schefter, with the first two years fully guaranteed at $32.5M.
Star quarterback Patrick Mahomes posted his immediate approval after news of the deal came out Monday.
Keeping pressure away from Mahomes has been a problem spot in each of the Chiefs' past two playoff losses.
Mahomes was pressured on 51.8% of his dropbacks in February's Super Bowl, the third-highest mark in a start of his career. He was pressured on 47.2% of his dropbacks in the 2018 AFC Championship Game against the Patriots, the fourth-highest mark in a start in his career.
Last season in Mahomes' starts, the Chiefs were 0-2 when he was pressured on more than half of his dropbacks and 16-0 when he wasn't.
The Chiefs in 2021 could have a completely different starting offensive line from last year's season opener. Tackles Mitchell Schwartz and Eric Fisher were recently released. Center Austin Reiter and guards Kelechi Osemele and Andrew Wylie can be free agents.
A fixture at left guard, Thuney, 28, never missed a game or a start in his five seasons with the Patriots, becoming the first player in NFL history to open his career by starting in three straight Super Bowls.
Between injuries and line shuffling, the Chiefs had five players play at least 100 snaps at guard last season.
Thuney, a 2019 Associated Press second-team All-Pro, has registered 5,474 offensive snaps since he entered the league, second only to Philadelphia Eagles center Jason Kelce's (5,492) during that same period. Thuney also filled in at center and right tackle in emergency situations, with his versatility one of his many assets.
He played the 2020 season under the franchise tag, earning a salary of $14.7 million.
Thuney, who speaks Spanish fluently, earned a master's degree in business administration while playing for the Patriots, who selected him in the third round of the 2016 draft out of NC State.
Information from ESPN's Mike Reiss and Adam Teicher was used in this report.