It will be his second spell in Cumbria, having previously enjoyed a loan spell there in the 2000/01 season. He made 30 appearances while on loan from Bolton, winning the Foxes' player of the year award.
That spurred Brian Little into signing him for City in a £50,000 deal, but he lost his place half way through the season. The appointment of Jan Molby gave him a second chance and he started the season as City's number 1, but was recently dropped.
Glennon made a parting shot at former manager Molby, citing his poor man management as his main reason for leaving.
He said: "I feel I was treated very harshly by him. One minute I was told I was his first choice for the rest of the season and the next I was dumped in the reserves without a word of explanation.
"It all went wrong when we lost at home to Macclesfield. I'll hold my hand up and admit I made a couple of mistakes in that game but I wasn't the only player who under-performed that night. Everyone made mistakes.
"Yet, I was the only player dropped for the next game. I was devastated but he never said a thing to me. I was singled out and I knew my future at the club was effectively over."
With Paul Musselwhite the only professional keeper still at Boothferry Park, Peter Taylor may search to add to his ranks. Grimsby shot-stopper Danny Coyne is one name rumoured to be shortlisted, while ex-City star Alan Fettis is also being linked with a move back to Hull.