Putin met earlier with Croatian President Kolinda Grabar-Kitarovic.
Ahead of the final in Moscow between France and Croatia, Putin has met at the Kremlin with Qatar's emir Sheikh Tamim bin Hamad Al Thani and Federation Internationale de Football Association president Gianni Infantino.
"It changed not only the perception of Russian Federation overseas, it changed us", Sorokin said.
The stadia aim to employ cooling technology capable of reducing temperatures within the stadium by up to 20 °C (36 °F), and the upper tiers of the stadiums will be disassembled after the World Cup and donated to countries with less developed sports infrastructure.
The tournament, which ends on Sunday with the final between France and Croatia at Moscow's Luzhniki stadium, has transformed "the perception that the world has about Russia", Infantino said.
On his part, Infantino expressed his content with the ceremony saying "It's so important that we can be here today in the iconic place of the Kremlin to pass the World Cup hosting rights from the organizer of the 2018 World Cup to the organizer of the 2022 World Cup".
SC have been shadowing and observing the 2018 World Cup operations in the 11 host cities, with over 180 professional studying the measures required in order to be prepared for the extravaganza four years later.
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"I'm sure that our friends from Qatar will be able to host the 2022 FIFA World Cup on the same high level".
"We are, of course, ready to share the experience we acquired in hosting the World Cup this year along with our friends, " the Russian President said.
As part of it's winning bid in 2010, Qatar promised to take apart numerous stadiums at the end of the World Cup and send sections to developing countries to help them grow the game.
"We hope to overcome all the difficulties", said the emir.
The emir says through a translator that the World Cup "will be a huge and great festival for all our country".
He said: "After a very hard year, seeing the country united these last few weeks has been fantastic".
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