The 32-year-old center had 43 points (11 goals, 32 assists) in 81 games with the Toronto Maple Leafs last season, and four points (two goals, two assists) in seven Stanley Cup Playoff games.
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"[Bozak is] a right-handed shot," Blues general manager Doug Armstrong said. "It gives us good depth now when you have [center Brayden] Schenn and Tyler, and we're hoping for [center Robert] Thomas to get that opportunity to push into that group, and other players. We just like the ability to add via free agency and not via trade, and Bozak's a quality player."
Signed by Toronto as an undrafted free agent on April 3, 2009, Bozak has 365 points (136 goals, 229 assists) in 594 NHL games and 10 points (five goals, five assists) in 18 playoff games.