It will be a competition that will provide an indication of which men's and women's nations might challenge for the ultimate Sevens prize - an Olympic gold medal.
The announcement comes on the eve of the IRB Junior World Rugby Trophy in Moscow, the first IRB fifteen-a-side tournament to be held in the country.
"Moscow has an exceptional history of delivering major international sports events and rugby is riding a wave of development in Russia thanks to the Olympic Games decision and their historic qualification for the 2011 Rugby World Cup 2011," added Lapasset.
"I am sure that this will be another memorable and successful sporting spectacle."
Rugby Union of Russia President Vyacheslav Kopiev said that it was a proud moment for his Union and the growth of the game.
"It is wonderful news to be selected as host Union for the 2013 Rugby World Cup Sevens," said Kopiev.
"The appointment to host the 2013 tournament is of enormous significance to Russian rugby.
"We are grateful for the trust that the International Rugby Board has shown us and accept this appointment with pride, passion and respect for the responsibilities that we will be undertaking on behalf of world rugby.
"We believe the appointment to host the Rugby World Cup Sevens tournament will, on top of Russia's qualification for the 2011 Rugby World Cup and the admission of Sevens into the Olympics, ignite the future of Russian rugby.
"The Rugby Union of Russia, with the support of our government, is committed to achieving our vision, that of Russia becoming a major rugby nation capable of competing on the world stage.
"I would like to express gratitude to our partners, the city of Moscow and the Russian Federal Government and to my colleagues within the Rugby Union of Russia who have worked so hard on putting our bid document and campaign together."
The 2013 event will be the sixth Rugby World Cup Sevens tournament. The inaugural competition was held in Scotland in 1993. Hong Kong (1997), Argentina (2001), Hong Kong (2005) and Dubai (2009) have also hosted the Sevens showpiece.
The decision by the International Olympic Committee to include Sevens in the Olympic Games, beginning in Rio in 2016, has provided an enormous boost to the game and planning is under way by the IRB on the required qualification process for international teams.
This forms part of a major overhaul of the existing IRB Sevens Strategic Plan, a collaborative process with all Unions that will outline the blueprint for the further growth of the game around the world in recognition of this significant development.
The Strategic Plan will allow the game to grow in new markets and ensure that all 117 IRB Member Unions can collaborate with their respective National Olympic Committees and have access to a structured development, tournament and qualifying pathway that optimises the effects of inclusion in the Olympic Programme.
The Rugby Union of Russia was one of eight nations to express a formal interest to host the 2013 Rugby World Cup Sevens tournament. Russia had previously bid to host the 2009 event.
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