Perron, 25, registered 10 goals and 15 assists in 25 games with the Blues this past season.
In 340 career NHL regular-season games over six season with the Blues, Perron has accumulated 84 goals and 114 assists for 198 points.
He was originally drafted 26th overall by the Blues in the 2007 NHL Entry Draft.
Paajarvi, 22, registered nine goals and seven assists for 16 points in 42 games with the Oilers this past season.
"Magnus is a well-rounded player who has good size and great skating ability," said Blues GM Doug Armstrong.
"He is just coming into his own and this will open up more ice time for Jaden (Schwartz) and Vladimir (Tarasenko). I would like to thank David for his time in St. Louis and wish him well in Edmonton."
Paajarvi was originally Edmonton's first-round pick (10th overall) in the 2009 NHL Entry Draft.