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The United States international enjoyed a successful loan spell with the Scottish champions last term, his seventh stint away from north London after turning out for the likes of Bournemouth and Swansea in the Championship.
“I am so pleased to complete my move to Celtic and I really could not be happier,” he told the Glasgow side’s website on Friday. “I have loved every minute of my time at Celtic so far and I really wanted to be part of the club’s future.
“We have a fantastic group of players at the club, we have a really good spirit and atmosphere among us and we all worked so hard together to deliver the league and League Cup success last season.”
Carter-Vickers played five games in total for Spurs, all coming in cup competitions having originally joined at the age of 11 and progressed through the academy. A club statement read: “We wish Cameron all the best for the future.”
Celtic manager Ange Postecoglou added: “I am absolutely delighted that the club has completed the signing of Cameron on a permanent basis.
“This is a major acquisition for Celtic, really positive news for us and everyone at the club has worked so hard to make this happen. Cameron has given everything of himself to the club so far, demonstrating his real value to the team and to the way we play.
“He was vital to our success during the season, such a hard working player of real quality and he was an absolute model of consistency.”