Two others signed free agent contracts.
Ware was selected by the Philadelphia Eagles in the third round as the 89th overall selection.
On Sunday, the second day of the draft, linebacker Brandon Chillar was chosen by the St. Louis Rams as the 130th pick overall. He'll be reunited with former Bruin linebacker Robert Thomas in St. Louis.
Nex was defensive end Dave Ball, who was chosen by the San Diego Chargers with the first pick of the fifth round (133rd overall). Not too long after, the New Orleans Saints selected defensive tackle Rodney Leisle as the 139th pick overall.