NFL Network first reported the agreement.
Waddle enters his sixth NFL season and has played in 45 regular-season games with 28 starts. He will compete for the Patriots' left tackle spot after Nate Solder signed a four-year, $62 million deal with the New York Giants.
The 6-foot-6, 315-pound Waddle was initially claimed on waivers by the Patriots on Dec. 16, 2015. He has mostly served as a backup, lining up at both left and right tackle.
In the 2017 season, when starting right tackle Marcus Cannon was placed on season-ending injured reserve, Waddle started four regular-season games and one playoff game on the right side.
At one point last year, offensive line coach Dante Scarnecchia referred to Waddle as a starting-caliber player, adding that "he's long, he's strong and he's got a good skill set."
Waddle was at the Patriots' facility last Friday for a physical, but then continued on to Dallas for a free-agent meeting with the Cowboys. Now he's back again.
He joins 2017 undrafted free-agent Cole Croston and six-year veteran Matt Tobin on the left-tackle depth chart. Offensive tackle Cameron Fleming, who has played in 47 regular-season games (20 starts) since being selected by the Patriots in the fourth round of the 2014 draft out of Stanford, is an unrestricted free agent.