It was confirmed on Tuesday night a fee had been agreed for the Belgian international after he was left out of the Fulham squad for their Capital One Cup defeat at Sheffield Wednesday.
And Dembele, who is viewed as a replacement for Luka Modric after his sale to Real Madrid, has now passed his medical and agreed personal terms.
The Belgian international midfielder added on Twitter: "Happy to confirm I signed a new contract with Tottenham FC!"
"I would like to thank all the Fulham fans for their support! You were amazing."
Earlier Tottenham said in a statement: "We are delighted to announce that we have reached agreement with Fulham for the transfer of Moussa Dembele."
Dembele joined Fulham in the summer of 2010 in a ?5million move from Dutch club AZ Alkmaar and has built a star reputation in that time.
Fulham said in a statement of their own: "The club can today confirm that it has reached an agreement with Tottenham Hotspur for the transfer of midfielder Moussa Dembele.
"The 25-year-old Belgian international has successfully completed a medical and will sign for an undisclosed fee.
"Following two full seasons at Craven Cottage, the club would like to thank Moussa for his contribution and wish him well throughout the rest of his career."
