The Flyers received second- and fourth-round picks in this weekend's NHL draft as well as a fourth-round choice next year.
The Blue Jackets get the promising Bobrovsky, who went 42-23-10 with a 2.73 goals-against average and .909 save percentage in two seasons with the Flyers.
The 23-year-old Bobrovsky was a solid backup to veteran Ilya Bryzgalov and could contend for a starting spot for the Blue Jackets, who are coming off a miserable season in which they finished with the worst record in the NHL.
Columbus gave up 3.13 goals per game in 2011-12, 28th in the league as veterans Steve Mason and Curtis Sanford struggled behind a porous defense.
The deal was announced on Friday.