Wannstrom, 23, was the 44th pick of the 2010 NHL Draft. He had five points in four games with the Kalamazoo Wings of the ECHL, and five goals and 10 points in 37 games with the Chicago Wolves of the American Hockey League last season.
The Blues also signed forwards John McCarthy and Pat Cannone.
McCarthy, 27, had one goal and one assist in 36 games with the San Jose Sharks last season, and seven points in 13 games with the Worcester Sharks, San Jose's AHL affiliate.
A 2006 seventh-round pick of the Sharks (No. 202), McCarthy has three goals and six points in 87 NHL games in parts of four seasons with the Sharks.
Cannone, 27, had 16 goals and 37 points in 59 AHL games with Chicago.