The Leafs had soured on backup Jhonas Enroth last month but hadn't found a real replacement to play behind starter Frederik Andersen who has started 33 of the team's 39 games this season, including three sets of back-to-backs.
The 27-year-old is on pace to start around 70 games, a substantial increase from his career high of 53 while with the Anaheim Ducks.
"We're trying to put a veteran in there that can take away some of those games that maybe (can) give (Andersen) a rest," Leafs general manager Lou Lamoriello told the Canadian Press.
After claiming McElhinney, the Leafs traded Enroth to the Ducks for a 2018 seventh-round draft pick.
As the Leafs searched for a backup goalie, veteran unrestricted free agent Karri Ramo was given a pro tryout and played three games with the AHL's Toronto Marlies. The former Calgary Flames netminder underwent major reconstructive knee surgery last season.
Ramo's agent Todd Diamond told ESPN.com Tuesday that Ramo will be out until late February after undergoing minor surgery to remove particles from that same knee.
The 33-year-old McElihnney was in goal on Saturday night when the Blue Jackets fell to the New York Rangers, who rallied from a 4-1 deficit and scored the winning goal with 17 seconds left.
He went 2-1-2 with the Jackets this season with a respectable .924 save percentage as the backup to Sergei Bobrovsky. He's earning $800,000 and will be an UFA July 1.
Information from The Associated Press was used in this report.