The hotel, which has been run by the Accor Hotels chain until now, will undergo a full renovation in the coming months at a cost of millions of euros in order to match it to the Leonardo Hotels' European concept.
The hotel includes 211 rooms and suites and will have a restaurant serving an international menu.
According to the agreement, the hotel will be operated by the Leonardo chain for 20 years.
The building is located at a short distance from most of the Austrian capital's main attractions, including the museum quarter, Hofburg Palace, the Technical Museum and the congress center.
Daniel Roger, general manager of Leonardo Hotels Europe, said Monday: "We entered a bid against 11 Austrian and German companies and we're very happy that we won.
"The hotel will now undergo renovation at a total cost of €5 million (about $6.5 million), which will include all rooms and public spaces. The hotel will include a large business lounge, a gym and a restaurant, and has an excellent location.
"The hotel's internal design will be planned by architect Andreas Neudahm, Leonardo Hotels' interior designer in Europe."
Roger added that in spite of the financial crisis in Europe, Leonardo's hotels in Germany ended the year with better results than expected.
"In the meantime we are not experiencing a slowdown in places like Berlin, Munich and other cities. Demands are high and we expect 2012 to be a good year as well," he said.
The Leonardo chain currently has 35 three-star and four-star hotels in Germany, Switzerland, Belgium and now in Austria.