Filatov was drafted sixth overall by the Blue Jackets in the 2008 entry draft. He had seven assists in 23 games played with Columbus last season.
The 21-year-old left-winger has a total of six goals and seven assists in 44 career NHL games.
The six-foot, 190-pound Moscow native also spent time in the Kontinental Hockey League, scoring nine goals and 13 assists with CSKA-Moscow in 26 games in the 2009-2010 season.
Columbus used the 66th pick acquired in the deal to select centre Thomas Tynan of Des Moines of the USHL.