Ian Rapoport of the NFL Network reported the expected signing Monday.
Oakland acquired Bryant as part of a trade with the Pittsburgh Steelers in April, but it cut him during its roster reduction to 53 players because he's facing a suspension for a violation of the league's substance-abuse policy, per ESPN's Dan Graziano.
The 31-year-old LSU product tallied 52 catches for 548 yards and three touchdowns while playing all 16 games for Cincy last season.
Pro Football Focus graded him poorly as the NFL's 96th-best receiver for 2017.
His best statistical campaign came in 2014 with the Pats when he tallied career-high totals in receptions (74), receiving yards (953) and TDs (seven).
LaFell will compete with Seth Roberts and Dwayne Harris for playing time behind projected starters Amari Cooper and Jordy Nelson once he gets up to speed with the Raiders offense.
It's unclear whether he'll be active when Oakland kicks off the regular season next Monday night with a home game against the Los Angeles Rams at Oakland-Alameda County Coliseum.