The 19-year-old defenseman, who was selected by the Vegas Golden Knights with the No. 15 pick in the 2017 NHL Draft, was acquired in a trade for forward Mark Stone on Feb. 25. Brannstrom has 29 points (seven goals, 22 assists) in 46 games in the American Hockey League this season.
Max Veronneau will also make his NHL debut for the Senators. The 23-year-old forward and Ottawa native signed a two-year entry-level contract on Tuesday after finishing his final season with Princeton University in the NCAA.
The Blues are in third place in the Central Division, four points behind the Nashville Predators with two games in hand, and five points behind the Winnipeg Jets. They are two points ahead of the Dallas Stars, who hold the first wild card into the Stanley Cup Playoffs from the Western Conference.