The 24-year-old United States centre-half has signed a four-year contract after an undisclosed fee was agreed with the Premier League club.
The USMNT defender hugely impressed during his season-long loan at Parkhead for the 2021/22 campaign, securing a place in the Scottish Premiership Team of the Year after helping the Hoops complete a domestic double.
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.”
Southend-born Carter-Vickers came through the Spurs youth ranks before loan spells with Sheffield United, Ipswich Town, Swansea City, Stoke City, Luton Town and Bournemouth.
He made one start for the London side at the start of the season, in a 1-0 defeat to Portuguese side Pacos Ferreira in the Europa League, only his fifth first-team appearance, before joining Celtic in September.
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.
“When we identify a player, we always hope that they can settle into things as quickly and as easily as possible, but like so many other players during the season, Cameron slotted into life at Celtic brilliantly from very early on.
“He is a great guy, hugely popular and we are delighted that he sees his future with us.”