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.
Dembele, who is viewed as a Spurs replacement for Luka Modric after his sale to Real Madrid, has now agreed personal terms and will make the move across London.
Fulham on Wednesday said in a statement: "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."
Dembele's move is reported to be worth in the region of £15million and Fulham could likely look to reinvest the money before Friday's transfer deadline.
The Belgian 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.
