Morris, 32, will become one of the youngest coordinators in the NFL.
After he returned to the Buccaneers in 2007, their pass defense jumped from 19th in 2006 to first last season.
"It was Christmas and I wanted to give him a Christmas present," Coach Jon Gruden told the Tampa Tribune.
Kiffin resigned earlier this month to join the staff of his son, Lane, who was named at the University of Tennessee to replace head coach Phillip Fulmer.
Monte Kiffin joined the Buccaneers' staff in 1996, and made its defense one of the NFL's best and most consistent, which gives Morris a daunting task.
Morris served in a variety of defensive roles from 2002-05 with other NFL teams.
"It's a great accomplishment and I'm proud they're giving me the keys to drive this defense," Morris said. "It's awesome."