Carney, 26, tasted step four success under Brown at Lancaster City and spent last season at Marine.
He said: “I know Phil, Macca and Rick, as well, and it will be good to get some games under my belt and hopefully help string together a run of results.
“I know they are meticulous in their approach and organise a team well and I’m looking forward to getting started.
“I see the team has some good results lately, beating Workington and then coming from behind to beat Sheffield in the Trophy. Hopefully we can kick on and keep a run going now.
“I’m quite ambitious myself and want to play as high as I can and do as well as I can.
“It hasn’t just happened at the minute and I need to be playing football and I want to be playing football.
“Hopefully I can get back playing and help Clitheroe get some wins as well.”
He trained with the Blues on Thursday night and goes straight into contention for the game at Pickering Town on Saturday.
Brown said: “He’s got a good engine, an eye for goal and he’s just really professional about everything he does. He will add to the squad and improve us.”
Striker Owen Watkinson is also available for the ninth-placed Blues following a three-match ban as Brown’s boys look for a third away win of the campaign at the bottom club.