The Republic of Ireland international has signed an initial four-year contract with an option for a further two taking the deal up to £7m.
Hoddle had been trying to sign a striker before Saturday's transfer window closed and, after been linked with a host of names his summer, the Spurs manager finally got his man.
Keane had vowed to fight for his first-team place under new Leeds boss Terry Venables during the club's pre-season tour of China.
But the forward had a change of heart when he found himself on the substitutes' bench for Leeds' first two games - and after talking with Hoddle about his plans for the club.
"I know I said I didn't really want to leave Leeds but when I came here to talk to Glenn his long-term plans appealed to me and that is why I am now a Tottenham player," said Keane.
"Glenn wants to take the club a long way and hopefully I can help.
"It was frustrating at Leeds. You want to play football and it would have been nice to play for them.
"But it was not to be and I am looking forward to playing for Spurs instead.
"This is a big club and Glenn has great ambitions.
"I am a striker so hopefully I can bring goals to the club, although I also believe I can make goals."
Keane was paraded to the Spurs fans before the start of Saturday's Premiership home game with Southampton although he is not eligible to play.
The signing will increase competition for places up front, where he will be challenging Teddy Sheringham, Les Ferdinand, Steffen Iversen and Sergei Rebrov for a place in the team.
Keane had a good World Cup this summer, scoring important goals for Ireland against Germany and Spain.