Fuller replaces Chris Ball, who left to become the head coach at Football Championship Subdivision program Northern Arizona.
Memphis coach Mike Norvell called Fuller "one of the top defensive minds in college football" in announcing the hire on Saturday.
Fuller has been at Marshall the last six seasons. He was assistant head coach and special teams coordinator from 2013-17 before becoming defensive coordinator in the 2018 season.
He was the defensive coordinator at FCS program Chattanooga from 2009-12.
Marshall allowed 21.8 points and 338.7 yards per game this season. Memphis allowed 31.9 points and 428.1 yards per game.