The 25-year-old shot-stopper joins the Blues as the second signing of the summer on a one-year contract with the option of a further year.
Mair joins United following a loan spell at the club during the second half of last season.
Speaking to club media, Mair said: “I’m delighted.
“I really enjoyed my five or six months here from January onwards. From day one, I enjoyed the club as a whole.
“You can see the direction it’s going in, and it feels like it’s trending the right way, so I’m really pleased to be back.
“I played the Brackley game and some of the behind-closed-doors games, and I felt I performed well.
“The club has rewarded me with a contract, and now I’m looking forward to kicking on.”
Mair began his career at Aberdeen before moving to Norwich City as a youngster.
During his time with the Canaries, he gained first-team experience through loan spells at King’s Lynn Town, Notts County and Gateshead before he joined Morecambe.
He arrived at Carlisle in January and featured against Brackley Town on the final day of the regular season, as well as in a number of behind-closed-doors fixtures.
Speaking to club media, Rob Elliot, head coach at Carlisle United, said: “I’ve worked with Archie before at Gateshead and know what he can bring.
“He is a goalkeeper with good presence, confidence and the ability to play with the ball at his feet.
“Having played in that position myself, I know how important mentality and consistency are, and Archie has shown he has the right character to keep developing.
“He is at a good stage of his career, with plenty of experience behind him but still a lot of room to grow.
“We’re looking forward to working with him again.”
