The Falcons also released veteran linebacker Ike Reese, who was used primarily on special teams.
The 6-foot-1, 255-pound Mughelli, who spent four seasons with Baltimore, agreed to a six-year, $18 million contract that includes a $5 million signing bonus.
49ERS: San Francisco signed cornerback Nate Clements, the star cornerback from the Buffalo Bills, to an eight-year, $80 million contract.
The 49ers also agreed to terms with safety Michael Lewis.
REDSKINS: Washington agreed to a contract after meeting with free agent linebacker London Fletcher and completed deals with three of their own players, safety Vernon Fox, guard Randy Thomas and fullback Mike Sellers.
PATRIOTS: New England released running back Corey Dillon, cutting ties with the top active runner in the NFL on the first day of free agency.
The Patriots also re-signed running back Heath Evans and guard Billy Yates. Terms of the agreements were not disclosed.
PANTHERS: Carolina re-signed linebacker Na'il Diggs to a one-year contract.
The Panthers also released safety Kevin McCadam, who played mostly on special teams last season.
RAIDERS: Oakland opened the free agency season by contacting representatives for quarterback Jeff Garcia, who has expressed an interest in returning to the Bay Area.
COLTS: Brandon Stokley, who was due a $500,000 roster bonus, and defensive tackle Montae Reagor, due about a $1 million roster bonus, became the first players to leave the Super Bowl champions after being cut.
LIONS: Detroit acquired another selection in April's draft, sending defensive end James Hall to the Rams for a fifth-round pick.
The Lions also made official the trade of cornerback Dre' Bly and a sixth-round pick to the Broncos for running back Tatum Bell, offensive tackle George Foster and a fifth-round pick.
BRONCOS: Jake Plummer, who lost his starting job during the 2006 to Jay Cutler season reportedly would rather retire than accept a trade to the Bucs, the NFL Network and other media sources reported.
BROWNS: Cleveland has agreed to terms with free agent offensive lineman Eric Steinbach on a seven-year, $49.5 million contract.
STEELERS: Pittsburgh decided not to pursue a free agent running back to complement Willie Parker, choosing instead to re-sign Najeh Davenport to a two-year contract.
JAGUARS: Jacksonville signed right tackle Tony Pashos and kicker Josh Scobee to five-year deals.
JETS: New York released seldom-used backup quarterback Patrick Ramsey.
DOLPHINS: Miami released defensive end Kevin Carter and guard Jeno James.