Patil would be in Switzerland till October 4 and then will travel to Austria for a state visit from October 4 to 7.
Prime Minister Manmohan Singh, Speaker Meira Kumar and External Affairs Minister S M Krishna were among a host of dignitaries who met her before her departure.
The President will be accompanied by a 45-member business delegation led by former FICCI President and Chairman of Modi Enterprises K K Modi, Minister of State for Parliamentary Affairs Rajiv Shukla, Members of Parliament Vijay Jawaharlal Darda, Prataprao Ganpatrao Jadhav, and Chinta Mohan.
Patil would also be visiting the prestigious European Organisation for Nuclear Research (CERN). The facility is one of the most important areas of research in particle physics.
During the trip, some agreements are also likely to be signed.
In Switzerland, the President will pay homage to Mahatma Gandhi on October 2 at his statue in Geneva.
While in Berne, the President will hold official talks with the President of the Swiss Confederation Micheline Calmy-Rey, and other members of the Federal Council.
The President will also unveil a bust of Rabindranath Tagore at the University of Lausanne on October 4.
An MoU is expected to be signed between the University and the Indian Council for Cultural Relations on setting up of Chair on Indian Studies.