Spurs and Fulham confirmed the transfer of Dembele for a fee reported to be in the region of 15 million pounds ($23.7 million) after the forward passed a physical and agreed to a five-year contract.
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."
The news followed a declaration by Hamburg that they would do everything possible to re-sign Van der Vaart from Tottenham before the transfer window closed.
Van der Vaart has been strongly linked with a return to his former club but the Bundesliga side's chairman, Carl-Edgar Jarchow, has admitted time is running out to convince Spurs to sell.
"There is not a lot of time -- it is really up to Tottenham Hotspur," he told Deutsche Presse-Agentur.
"If we have a chance to sign him, we will do everything we can to make that happen."
That opportunity could present itself now that Tottenham has successfully began to sign some of their own targets during what looks set to be another frantic final 48 hours of a summer transfer window at White Hart Lane.
As well as triggering the release clause for Dembele, Villas-Boas has also renewed the interest in Shakhtar Donetsk forward Willian, who could fill the void left by the departure of Luka Modric.
Shakhtar chief executive Sergei Palkin on Wednesday claimed he had rejected a bid of just under 12 million pounds ($18.9 million) for the Brazilian and that Tottenham chairman Daniel Levy had also made an inquiry about two other players.
"Mr Levy, the chairman of Tottenham Hotspur FC, personally flew to Donetsk to negotiate over Willian," Palkin told his club's official website.
"Levy, by the way, hinted that besides Willian, Villas-Boas was interested in Douglas Costa and Fernandinho, but he mentioned that just casually, without any specifics," he added.
Spurs have been heavily linked for some time with France goalkeeper Hugo Lloris and there are reports they could be on the brink of agreeing on a deal with Lyon in the region of 13 million pounds.
Van der Vaart is said to be valued at around 14 million pounds ($22.1 million) by Daniel Levy, almost double what the Tottenham chairman paid Real Madrid for the 29-year-old two years ago.
The Holland star joined Real from Hamburg, where he became a cult hero during his three-year spell at the club, while his wife, Sylvie, still works in Germany.
Spurs have also been linked with Internacional striker Leandro Damiao and Rennes midfielder Yann M'Vila but the chances of them moving to White Hart Lane appear to have receded.
Time is also running out for Villas-Boas to offload players, with doubt having reportedly been cast on the futures of several players, including Michael Dawson, Jermaine Jenas, Aaron Lennon, David Bentley, Heurelho Gomes, Giovani dos Santos and Jermain Defoe.
Tom Huddlestone appeared to have completed a loan move to Stoke, although that has been complicated by his physical that prompted concern over his long-standing ankle problems.