On Saturday morning Tottenham also confirmed that winger Aaron Lennon has signed a new contract which commits him to the club until 2016.
"We are delighted to announce we have reached agreement with Fulham for the transfer of Clint Dempsey," Spurs said on their website.
The 29-year-old had been strongly linked by the media with a move to Liverpool following his 17-goal haul in the Premier League last season but the Anfield club failed to meet Fulham's transfer evaluation.
Dempsey joined Fulham in 2007 from New England Revolution, scoring 60 goals in 224 appearances for the Craven Cottage team.
Earlier in the evening, Spurs agreed to pay Lyon a fee of £10 million for France number one Lloris, plus possible add-ons worth £5m.
"Lloris has signed a four-year contract," Lloris's former club Lyon said on their official website.
Lloris, 25, who has won 38 caps and featured at the 2010 World Cup and Euro 2012, joined Lyon in 2008 from Nice.
He won Ligue 1's best keeper award in 2009, 2010 and 2012.
Midfielder Van der Vaart, 29, previously played at Hamburg from 2005 to 2008 before leaving to spend two seasons each at Real Madrid and Tottenham.
"I'm enthusiastic that Rafael van der Vaart is playing for HSV again," said Thorsten Fink, favourite to be the first coach to lose his job in the Bundesliga this season. "He will be an important reinforcement for our team."
Van der Vaart, a regular with the Dutch national team for a decade, said on the club's website: "This is a dream for me and my family. I'm looking forward to three great years."
Having finished third, seventh and fourth in the three years Van der Vaart played for them, Hamburg, the only ever-present side in the Bundesliga's 50-season history, narrowly avoided relegation last season as they finished 15th.
They have also made a poor start this term, losing at home to Nuremberg in their Bundesliga opener on Saturday and getting knocked out of the German Cup by third tier Karlsruher the week before.
The news came hours after Van der Vaart was dropped from the Dutch squad for next month's World Cup qualifiers against Turkey and Hungary, with coach Louis van Gaal saying he had not played enough club football recently.
Also moving on is defender Danny Rose who has joined Sunderland on a season-long loan while Real Mallorca have agreed to sign Mexico forward Giovani Dos Santos on a four-year deal.
Lennon, 25, has played more than 230 matches in all competitions for Spurs since joining from Leeds in 2005.
He has started both Premier League matches for Andre Villas-Boas's side this season.
- Aaron Lennon