The Canaries were beaten 5-0 on the opening day of the Premier League campaign and the French-born Cameroon international will add some much needed cover for new boss Chris Hughton, who worked with the 26-year-old at Newcastle.
Bassong wrote on his Twitter feed: "I've been officially transferred to Norwich today. 3 years deal. another chapter in my football life.
"I wish all the best to my old team mate at Spurs. I've had great time with them. I hope they'll success."
Norwich confirmed the transfer on their official website just after noon.
Bassong started his career at Metz, before signing with Newcastle in a ?500,000 deal during the summer of 2008 and was voted their player of the season in his first campaign with the club.
An ?8million move to Tottenham followed when the Magpies were relegated, but the defender found his chances limited last season and so spent a spell on loan with Wolves.
Hughton feels Bassong will bring some much needed depth to the Norwich defence as the Canaries look to build following the departure of manager Paul Lambert to Aston Villa in the summer.
"Sebastien is a player that I have known well since my time at Newcastle and I'm delighted to have brought in someone with the Premier League experience he has got," Hughton said on canaries.co.uk.
"He will give us power and pace at the back and again add to the competition in the squad."
Last week, Norwich signed former Manchester City left-back Javier Garrido on loan from Lazio and have been scouting Blackburn goalkeeper Mark Bunn, who is reported to have handed in a transfer request.