Earlier in the day, Donbass terminated the contract of goalie Chris Holt to make room for Leighton on the roster.
Leighton played in just one game with the Flyers in 2012-13, recording a loss.
With Vezina Trophy winner Sergei Bobrovsky between the pipes in Columbus, and netminder Curtis McElhinney set to serve as the club's backup, there was no room for Leighton on the Blue Jackets.
In 105 career NHL games with the Flyers, Nashville Predators and Carolina Hurricanes, Leighton registered a 35-41-4 record with a 2.97 goals-against-average and a .901 save percentage.
Leighton was originally drafted by the Blackhawks in the sixth-round (165th overall) of the 1999 NHL Entry Draft.