The Flyers will get the Jackets' 45th overall pick in Saturday's second round plus the 117th overall this year as well as the fourth-round pick next year (pick previously acquired from Phoenix).
The two-day draft begins Friday night in Pittsburgh.
Bobrovsky, 23, has appeared in 83 career NHL games with the Flyers, compiling a 42-23-10 record with a 2.73 goals-against average and .909 save percentage.
A native of Novokuznetsk, Russia, Bobrovsky played four seasons with Metallurg in Russia from 2006-10. He registered a 2.74 GAA and three shutouts in 99 career games. He also helped Russia to a bronze medal in the 2008 World Junior championships.