The Titans now have five players from their six-player draft class under contract with first-round choice Isaiah Wilson as the lone player unsigned.
Tennessee selected Fulton in the second round, using the 61st overall choice on the LSU star.
He started all 15 games for the Tigers in 2019 and made 38 tackles, 14 pass breakups and one interception. He earned second team All-SEC honors.
Fulton ran a 4.46 at the NFL Combine.