The Flyers received a second-round draft pick in 2007 in exchange for Biron while the Blue Jackets got Buffalo's fifth-round selection in '07.
Biron was pulled aside and informed of the trade while the Sabres were in Toronto preparing to play the Maple Leafs.
"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."
An eight-year NHL veteran, Biron has been seeking a trade since losing the No. 1 job to Ryan Miller early last season. And the injury-depleted Sabres have been looking to free up payroll because they are at the NHL's US$44-million salary cap.
"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."
Miller said he was excited for Biron but a little disappointed, too.
"I really feel like he's a huge part of the Sabres," Miller said.
"It definitely wasn't Marty's personality or his play - it was definitely the business side of things," Miller said. "He's been a huge part of the reason we've been successful and we're going to miss him a lot."
Biron, who is making $2.1 million this season, proved expendable because he is in the final year of his contract and eligible to become an unrestricted free agent this summer.
Buffalo's first-round pick in the 1995 draft, Biron is the Sabres' longest-serving player.
He has a 12-4-1 record and 3.04 goals-against average this season. His career record is 134-115-25 with four overtime or shootout losses, a 2.53 goals-against average and 18 shutouts.
Biron struggled in his last outing, allowing four goals before being pulled in the second period in a 6-5 loss at Ottawa on Saturday.
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 $525,000 this season.