The Dutch midfielder played for the Bundesliga club between 2005 and 2008, scoring 48 goals in 113 games before moving on to Real Madrid, and then to the Barclays Premier League.
After penning a three-year contract with Hamburg on transfer deadline day, van der Vaart said it was great to be back.
"It feels a bit like I am coming back home," he said. "Everybody knows that I still have a strong bond with Hamburg and it is a compliment when a club wants you every year.
"This season was the right time."
The deal, which has partly been financed by a local investor, went through today after the Dutch player passed a medical in the northern Germany city after the two clubs agreed terms late last night, paving the way for him to make his second debut for Hamburg against Werder Bremen tomorrow.
"It was a very, very hectic night and I had to race to the airport this morning to get to the medical," he told hsv.de.
"If everything goes according to plan, then maybe I will travel (to Bremen tomorrow), but to be honest, I have only been here a few hours and we will just have to wait and see."
Van der Vaart has been included in Thorsten Fink's squad and the attacking midfielder is just the man the Hamburg coach wanted after two consecutive defeats.
"I am delighted that Rafael van der Vaart will be playing for Hamburg again," he said. "He will be a strong addition to our team."
The deal was made possible by a local investor, who had also contributed to the transfers of Heiko Westermann, Marcell Hansen, Dennis Aogo, Dennis Diekmeier and Lennard Sowah.
Klaus-Michael Kuhne gave the Bundesliga club an interest-free loan to enable them to match Tottenham's asking price for the Dutchman.
Hamburg started the season - their 50th consecutive year in the Bundesliga - with a 1-0 defeat at home to Nurnberg after being knocked out of the DFB-Pokal in the first round.
Hamburg's poor start convinced them to make an extra effort to sign van der Vaart, who was a big crowd favourite during his first spell at the club before moving to Real Madrid.
"In view of the sporting situation of the team and the perspectives, we came to the conclusion that we had to complete this transfer," read a statement from the club's board of directors.
"This was only possible thanks to the generous financial assistance of Klaus-Michael Kuhne."
However, the 29-year-old has warned that he cannot perform miracles and that the fans should not expect results to arrive overnight.
"Of course I am no superman, (Lionel) Messi or (Cristiano) Ronaldo," he said. "But I do think that I can help the team.
"I have always followed Hamburg's progress and I think that the team is good. There are many talented players, but self-confidence is lacking.
"I hope that we can get that back with me here and that we can have a great time together.
"This return to Hamburg is a dream come true for me and my family. I am looking forward to three great years."