Young athletes aged 15 to 18 were greeted by International Olympic Committee chief Thomas Bach at a ceremony near the Obelisk, a historic monument.
"This experience will stay with you for all your life. We are all assembled here to celebrate you, as the real game-changers," he said in the address.
The ceremony ended with the lighting of the cauldron with the Youth Olympic flame followed by a splendid firework display.
"Taking part in these high-profile competitions is a special honor and great responsibility. Hard work and stamina helped you achieve impressive results and join Russia’s national team," he said.
"I sincerely congratulate your united closely-knit team, which represents practically all sports, on your well-deserved ticket to the Games," the president added.
The games will close on October 18. They will feature many new disciplines, such as BMX freestyle, kiteboarding, futsal, climbing, roller sports, and competitive break dancing.