Celtic have confirmed Forster has signed a four-year contract, although the player himself had already done so earlier in the week.
Forster has spent the last two seasons on loan at Celtic Park from Newcastle but the end of his long-running saga over his permanent transfer confirms the club's first summer signing.
Lennon told the club's official website: "We are delighted that Fraser has committed his future to the club and we believe he will be a magnificent addition to the squad.
"He gives us that continuity so this is something we are really pleased about. He is a top-class keeper."
Forster, 24, added: "This is a massive club and I feel like this is a step forward in my career.
"I want to win things as a team and improve as an individual and I think I will be able to do that at Celtic.
"It also gives me a great opportunity to play in the Champions League if we get through the qualifiers. I really enjoyed my time in Europe last season so I will be looking forward to it if it happens again.
"I enjoyed last season as a whole and we have a great young squad here.
"The players and the coaches make it an enjoyable place to be and I like being a part of this team."
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