The 24-year-old defender joined the Hoops initially on a season-long loan last summer and played a crucial role in delivering the Scottish Premiership title and League Cup to Parkhead.
The centre-back, who is currently on international duty with the United States national team, has now committed his long-term future to the Scottish champions amid strong transfer interest from various English Premier League clubs.
GlasgowWorld understand Celtic agreed on a fee believed to be around £6million with the potential to rise to £10million and confirmed his signing after teasing a post on social media this evening.
Carter-Vickers, who joined the Spurs at the age of 11 before was fast tracked into the first-team under Mauricio Pochettino in 2016, has spent the majority of his career out on loan after making SEVEN temporary moves away from the London club.
He will now look to build on the strong partnership former alongside Carl Starfelt at the heart of the Celtic defence ahead of playing in the Champions League next season.
He told the club website: “I am so pleased to complete my move to Celtic and I really could not be happier.
“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.
“I wanted to make sure I was part of this group going forward and working under a great manager, and now we all want to achieve more.
“We have so much to look forward to, we will aim to be strong again domestically and of course we look ahead with real excitement to the Champions League.
“I have received such a great welcome from everyone at the club from day one and also from our supporters. When you are fortunate enough to be inside Celtic you can see it really is one of the world’s great football clubs.
“I am delighted to be given this opportunity at a club of this stature and I will be doing all I can to play my part in bringing more and more success to our fans.”
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.”
The manager added: “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 in to 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.”