The St. Louis Post-Dispatch reports it is worth $2.4 million.
Paajarvi, who was acquired in a trade July 10 for David Perron, was a restricted free agent.
"Magnus is a well-rounded player who has good size and great skating ability," Blues general manager Doug Armstrong said after acquiring Paajarvi from the Edmonton Oilers.
Paajarvi scored 16 points (nine goals) for the Oilers last season in 42 games. The 22-year-old has 26 goals and 32 assists in 163 NHL games.
He was the 10th pick of the 2009 NHL Draft.
"Our team is built on balance," Armstrong said. "We think [Magnus] can come in here and provide an element we don’t have right now. ... We think Magnus is just entering the guts of his career right now. We're looking forward to him being a Blue."