The 25-year-old midfielder was reportedly the subject of a £15m bid from Tottenham earlier this week, and the north London club's negotiations with their capital city counterparts have been successful.
Dembele becomes Andre Villas-Boas' first signing since the sale of Luka Modric to Real Madrid, and the Belgian should slot straight into the Tottenham midfield.
A classy midfielder with a keen eye for a pass, Dembele reportedly attracted interest from a number of Premier League clubs, including Manchester United.
But, following Modric's departure, Villas-Boas has moved quickly to secure midfield reinforcements, and Dembele should occupy an attacking midfield role at White Hart Lane. Despite the announcement, Spurs are still expected to be among the busier clubs as the transfer windows draws to a close.
France international Hugo Lloris is expected to decide on his future within 48 hours, while AVB reportedly wants to sign Porto star Joao Moutinho and Russian ace Alan Dzagoev.
But, with three days to go until the deadline, Dembele becomes the first confirmed signing.
A product of the Germinal Beerschot academy in Belgium, Dembele earned a move to the Eredivisie with Willem II in 2005, before joining AZ Alkmaar a year later.
After winning an Eredivisie championship with AZ, the Dutch club agreed a fee in the region of £5m to take Dembele to Fulham in 2010, where he was converted from striker to midfielder. The transition paid dividends, and Dembele has won praise for his accomplished displays, his performance against Manchester United last week a particular highlight.