Kostin recently wrapped up the KHL season and helped Avangard Omsk claim their first Gagarin Cup on Wednesday.
In 24 playoff games, Kostin registered nine points (five goals, four assists) and a plus-5 rating. He also posted 99 hits in the postseason.
Kostin was assigned to the KHL in September when the NHL's 2020-21 season was still uncertain due to the coronavirus. He will be required to quarantine before joining the team.
"Obviously, he played real well over there," Blues Head Coach Craig Berube said of Kostin. "They won a championship and he was a big part of it. He's the type of guy, we really like his size and strength, just his heavy play. So he's definitely a guy that I think could help our hockey team."
"But we've got to get him in here and get him acclimated and get him going and we'll see from there."
Kostin was drafted by the Blues in the first round (No. 31 overall) of the 2017 NHL Draft. He has played in four regular-season games with the Blues and has recorded one goal.
In three seasons with the AHL's San Antonio Rampage, Kostin has 29 goals and 53 assists (82 points) in 181 games.
