Frazier agreed to join Smith's staff less than a week after being fired by the Vikings, after more than three seasons on the job.
Frazier, 54, was the Vikings defensive coordinator from 2007 until taking over as head coach during the 2010 season. The Vikings allowing 30 points per game this season, worst in the NFL, the St. Paul Pioneer Press said.
NFL.com said Saturday Smith had been looking at Dallas assistant Rod Marinelli to to run the defense in Tampa Bay but the Cowboys refused to let Marinelli out of his contract.
Marinelli was Smith's defensive line coach when Smith coached the Chicago Bears.
The Bucs Friday finalized a two-year contract for Jeff Tedford, the former Cal coach, who will become Smith's offensive coordinator.
2014: The Year in Music [PHOTOS]