The 53-year-old links up with the Cumbrians after helping Fleetwood Town avoid relegation from League One at the end of last season.
Sheridan succeeds Keith Curle, who left the League Two outfit at the end of the 2017-18 campaign after three-and-a-half-seasons in charge.
"There are challenges for the club, but I'm going to face them head on," Sheridan told the Carlisle website. "I'm really proud to be Carlisle's new manager.
"I've no hesitation saying that my hopes are to get Carlisle promoted. I have ambition, vision and want to establish a strong DNA within the football club."
Sheridan has also previously managed Oldham Athletic, Notts County, Plymouth Argyle, Newport County and Chesterfield.