"I am proud and honoured that I am able to introduce Alberto Contador to our team next year," Riis told a news conference.
"It is an impossible opportunity that has occurred and that we are able to realise."
"I am proud to be able to attract the world's best to a Danish cycling team," added Riis.
Spaniard Contador announced last week he would not renew his contract with Kazakh-funded Astana who he joined in 2008.
"I think I've chosen the best option and I'm confident that Riis will build a great team in 2011," Contador said in a statement.
Contador won his third Tour de France title last month, finishing the three-week race 39 seconds ahead of Saxo Bank team leader Andy Schleck.
Riis said he was convinced that Contador's full potential is yet to be seen and added that he has great ambitions for the Spanish rider.
"It is obvious that we are going for the Tour de France, but Alberto told me a while ago that his ambition is to win all the three major tours in one year," Riis said.
Italy's Giro d'Italia and Spain's Vuelta a Espana are the other two major stage races in cycling.
"I am not sure it will be next year but one of the following years it is our ambition - and I believe it can be done," Riis said.
Luxembourg rider Schleck, also runner-up to Contador in 2009, and his brother Frank have said they will leave Team Saxo Bank at the end of the season.
Riis declined to say whether other new riders would follow Contador into the Saxo team.
Saxo Bank will remain a co-sponsor of the team, which has also enrolled US software group SunGard as a co-sponsor.
The announcement reversed a January decision by Saxo Bank to drop its sponsorship of the cycling team at the end of 2010.
"The team will be called Saxo Bank-SunGard Professional Cycling Team," Saxo Bank said in a statement.
"With these two companies committed to the team, we have a solid financial foundation for the future," Riis said.
Riis won the Tour de France in 1996 but in 2007 he admitted using banned drugs.