The visit will see him touring several countries, including the UK and France, comes closely after his comments on the return of monarchy in Nepal sparked much outrage in the country.
Gyandra left last evening and will reach France via Doha on a Qatar Airways flight, sources close to the former King said.
All his family members, except his son and former Crown Prince Paras, are accompanying him on the trip. Accompanying him are his wife Komal, daughter-in-law Himani, daughter and grand-children.
Although the purpose behind the trip has been disclosed, he is likely to meet some political leaders during the visit, the sources said.
This will be his first visit to Europe after the abolition of monarchy in May 2008.
The former King had visited India thrice after renouncing the crown.
The former King had recently come under fire from senior leaders of political parties after his remarks that monarchy can stage a come back in Nepal.