Rattie was the Blues' first selection at the 2011 draft, taken in the second round and 32nd overall.
Rattie, 19, led the Western Hockey League's Portland Winterhawks and ranked third overall in league scoring with 121 points (57 goals, 64 assists) during the 2011-12 regular season.
The six-foot, 173-pound Calgary native added a league-leading 19 goals in 21 playoff games as the Winterhawks advanced to the WHL final.
"Ty had a great offensive season and an impressive performance in the playoffs," Blues GM Doug Armstrong said in a statement. "We are excited about his potential and look forward to him joining our organization."