Forster was on loan at the Glasgow club last season and will return for another campaign on loan with a view to a permanent move.
Ahead of their Europa League play-off first leg against Swiss side Sion at Parkhead, Lennon said: "A deal has been agreed.
"There are a few little snags to overcome but we hope to have him registered in time for tomorrow night."
Lennon continued: "If that is the eventuality of things, we would be absolutely delighted.
"He has been the main target since the end of last season. We did put a bid in but it was knocked back but we worked hard in the background to try to bring him in so I'm very, very pleased."