The 26-year-old agreed a two-year deal and will be registered on September 1 when the club's embargo is lifted.
The French-Tunisian spent time with McCoist's squad in Brora and in Germany this summer and impressed the Ibrox coaching team sufficiently to earn a contract.
He joined Jon Daly, Nicky Clark, Nicky Law, Steven Smith, Richard Foster, Arnold Peralta and Cameron Bell as new faces in the Light Blues group.
Mohsni will not be eligible to feature until the transfer embargo ends but will continue to train with the squad in the interim ahead of the club's Scottish Second Division campaign.
He said: "I'm very happy to sign for Rangers. I have agreed for two years and I think it is a chance to prove that I can play in the top league and be a part of the squad.
"It would be amazing to be one of the players who help Rangers back to where
"It's a great squad with a great atmosphere so I've enjoyed it a lot because all of the players welcomed me very quickly.
"I felt like part of the squad from the first day so I've very happy to sign
and stay with that team.
"Sometimes when you feel happy like that you play better and I felt that way
from the first day so maybe that helped me decide to stay."