The four-year veteran, who signed a one-year deal, is the second free agent tackle added by the Bengals in recent weeks. Cincinnati last month signed nine-year veteran Michael Myers, a well-regarded tackle, to a two-year, $1.65 million contract. The Bengals also chose former Oregon defensive tackle Matt Toeaina in the sixth round of the draft.
Financial details of Allen's contract were not yet available.
Allen, 28, joins what is becoming a crowded tackle depth chart and will have to battle for playing time behind starters John Thornton and Sam Adams, along with second-year pro Domata Peko and Myers. Their newfound depth at the position could precipitate a move by the Bengals to thin out the position in coming days.
In 31 games, Allen has 54 tackles, three sacks and two fumble recoveries. The former LSU standout entered the league as an undrafted free agent with the New Orleans Saints in 2003, then played two years with the New York Giants (2004-2005), before signing with Green Bay last summer.
Allen appeared in just two games with the Packers, however, before suffering a season-ending foot injury.
At 6-feet-5, 328 pounds, Allen is built more like a nose tackle but is quick enough to also play some at the "under" tackle spot. His strong suit is defending against the run, but his three sacks in limited playing time demonstrate some ability to push the pocket inside.
Three other teams showed interest in signing Allen this spring.
Senior writer Len Pasquarelli covers the NFL for ESPN.com.