President of the Russian Olympic Committee Leonid Tyagachev and Moscow Mayor Yury Luzhkov have signed a written request for the International Olympic Committee (IOC) to register the bid.
Russian Deputy Prime Minister Alexander Zhukov pledged that the government would provide all the necessary guarantees if Moscow's bid is successful.
The IOC approved the decision to hold the Youth Olympic Games every two years at its 119th session July 5, 2007.
"This is a historic moment for the Olympic Movement. We owe this to the youth of the world," IOC President Jacques Rogge said after the vote.
Early last month, Russia's Black Sea resort of Sochi won the bid to be the venue for the 2014 Winter Olympics, the first winter games for Russia.
In 1980, Moscow hosted the Summer Olympics but the event was marred when over 60 countries boycotted the games over the war in Afghanistan.
