Norwich confirmed via their Twitter feed that they had completed the signing after securing an extension on the 11pm deadline.
Kane spent a period on loan at Millwall last season, scoring eight goals in the Championship.
Norwich boss Chris Hughton said that he was happy with the deal.
"I'm delighted to bring in someone of the quality of Harry," Hughton told the club's official website. "He is a very talented young player with bags of potential.
"He enjoys scoring goals as he has shown coming through the ranks at Spurs and during some good loan spells."
Kane, who has represented England Under-19s, previously worked with Hughton during the manager's time at Spurs.