The agreement is worth $700,000 at the NHL level and $70,000 at the American Hockey League level.
Stevens, a fifth-round draft pick of the Blues at the 2016 NHL Draft (No. 125 overall), played in 59 games with the AHL affiliate San Antonio Rampage last season, posting nine goals and nine assists (18 points).
Prior to turning pro, Stevens played four seasons of NCAA hockey at Northeastern University, where he recorded 57 goals and 61 assists (118 points) in 132 games.