The League Two side sit rock bottom of the Football League and are yet to win a game in the fourth tier this season.
However, Curle has been appointed on a contract that runs until the end of the 2015-16 season in what will be his fifth managerial role since retiring as a player.
The former England international began his coaching career as a player-manager at Mansfield Town - Carlisle's opponents on Saturday - before taking charge of Chester City, Torquay United and Notts County.
Curle left his role with County in February last year.
Carlisle's managing director John Nixon said the club's board has every confidence that Curle and his assistant Colin West have the capabilities to turn the team's form around over the remainder of the season.
"It is good to have the appointment made because, as I said the other day, it’s a dynamic situation and things are changing all the time," he told the club's official website.
"We've been through quite a long interview process, which has lasted for nearly a week, because we felt it was important for us to identify and appoint the person we felt was the right man for the job.
"We think we’ve got that in Keith Curle and his assistant Colin West. He has a good record of pulling squads together and making them play well, and his win and draw ratio at Notts County was very good.
"There is a firm belief that we have now have the foundations in place not only to get away from bottom place but to make significant moves up the table. Keith knows we feel that and he agrees it is more than achievable."
