It wasn't immediately clear what the Flyers were giving up in exchange for Biron or what the Sabres were sending to Columbus for Conklin.
"I feel I have some good experience and I can really help out and move forward," Biron said. "I definitely want to see the Flyers move ahead and get successful."
A source confirmed the deal involving Conklin, who be Ryan Miller's backup in Buffalo.
"You always want to play and I felt like I could do more for the organization," Biron said of playing a backup role in Buffalo. "They gave me a shot this year to be able to be part of it a little bit more but at the end, it was understandable that something had to be done."
The move gives Buffalo some much-needed salary cap room. Biron, 29, is earning US$2.1 million this season while Conklin is bringing home just $525,000. Prior to the deal, the Sabres' payroll was right at the $44-million cap limit.
Biron, who is due to become an unrestricted free agent July 1, was 12-4-1 this season with a 3.04 goals-against average and a .899 save percentage.
Conklin, 30, is 2-3-2 with a 3.30 GAA and an .871 save percentage for the Blue Jackets this season. He is earning this season.