The 39-year-old former Republic of Ireland midfielder has been acting as caretaker boss since the start of September, having been with the Cumbrian club as player, player-coach and assistant manager to Greg Abbott since 2009.
"We spoke to Graham on Saturday afternoon, as soon as his preparations for the Notts County game had been completed, to inform him that we wanted to offer him the position as first-team manager win, lose or draw on Saturday," managing director John Nixon said on www.carlisleunited.co.uk.
"I think everyone at the club has been impressed with the way Graham has applied himself and in the way he has placed his own stamp on the role under difficult circumstances."
Carlisle made it three wins in a row under former Middlesbrough, Stoke, Cardiff and Sunderland midfielder Kavanagh by coming from behind to beat struggling Notts County 2-1 at Brunton Park on Saturday.
- Sports & Recreation