Burkhead entered the NFL as a sixth-round draft choice out of Nebraska in 2013. At 5-foot-10, 210 pounds, he could be eyed to fill Brandon Bolden's role in New England as a reserve running back and special-teamer.
Burkhead reflected on the signing in a tweet.
Just want to thank the Bengals org. for everything the past 4 years. All class. Excited for the opportunity to compete in New England.
— Rex Burkhead (@RBrex2022) March 14, 2017
Burkhead had 74 carries for 344 yards and two touchdowns and 17 receptions for 145 yards last season. He played 22 percent of the team's offensive snaps in 2016 and 47 percent of the special-teams snaps.
Burkhead, who turns 27 on July 2, was primarily a special-teamer in his first three NFL seasons, before injuries to Jeremy Hill and Giovani Bernard opened opportunities for him on offense last season.
"I'm confident in my skills," Burkhead said last season, according to the Cincinnati Enquirer. "I know what I can do; just needed an opportunity. For me, it came Year 4 into the NFL, so I've been patiently waiting for it and just did my best out there when I got the chance."
At running back, the Patriots have Dion Lewis, James White, D.J. Foster and Tyler Gaffney under contract for 2017. LeGarrette Blount and Bolden are unrestricted free agents, and Lewis and White are scheduled for unrestricted free agency after the 2017 season.
ESPN's Katherine Terrell and Mike Reiss contributed to this report.