Evans, the No. 22 overall pick out of Alabama, signed a four-year contract with a fifth-year option. He is expected to receive a contract worth $11.7 million with a signing bonus of $6.59 million.
The 6-foot-3, 232-pound Evans was an integral part of the defense for the national champion Crimson Tide last season, registering 74 tackles, including 13 for loss and six sacks.
A second-team All-Southeastern Conference selection, Evans appeared in 53 career games for Alabama and recorded 152 tackles, 15 sacks and 19 quarterback hits.
Tennessee made a trade with Baltimore to move up three slots in the first round to take Evans, who filled a major need after the Titans lost linebacker Avery Williamson to free agency.
The Titans have signed three of their four draft picks. Linebacker Harold Landry, their second-round selection, remains unsigned.