Ian Rapoport of NFL Network reported a deal had been struck, though financial terms were not immediately known.
The 35-year-old Incognito announced his intention to retire in April. The Bills originally placed him on the retired list, but the sides went through a tense month after Incognito announced he had changed his mind.
He said he did not want to play for the Bills and waited until the team released him.
"I'm done. That's it. It's been a long career," Incognito told Vic Carucci of the Buffalo News. "Went to the doctor. My liver and kidneys are shutting down. The stress is killing me. It's just about doing what's right. I just want to be in the Hall of Fame."
Incognito made the Pro Bowl in all three of his seasons with the Bills from 2015 to 2017. It was the most successful stretch of a career that has also taken him to the St. Louis Rams and Miami Dolphins, and it marked a turning point after he sat out the entire 2014 season because of the fallout from a bullying scandal while with the Dolphins.
In August, Incognito was arrested after allegedly making threats to shoot people at a funeral home where his father's body was being held. He was sentenced to 11 months' probation after pleading guilty to disorderly conduct.
Oakland will likely slot Incognito into a position where he'll either start or not make the roster. He was originally scheduled to make $3.7 million with the Bills in 2018.