The pick becomes a third-rounder if Edmonton makes the playoffs this season, a source told ESPN.com.
The Leafs needed to open up a roster spot with the return of Matt Frattin from injury.
Brown, 27, adds grit to an Oilers lineup that has been lacking it up front. The rugged forward had 70 penalty minutes in 12 games for Toronto this season, including five fighting majors. In 254 games with Vancouver, Anaheim and Toronto, he has 14 goals, 11 assists and 519 penalty minutes.
Information from The Associated Press was used in this report.