In a Kremlin ceremony broadcast on television, Putin thanked "all those who helped making this dream come to life," including the head of soccer's global governing body.
Infantino, with the Order of Friendship medal pinned to his lapel, replied: "You welcomed the world as friends, and the world has created bonds of friendship with Russia that will last forever."
Russia's successful 2010 bid to host the 2018 tournament, which FIFA oversaw under Infantino's discredited predecessor Sepp Blatter, was marred by allegations of corruption in the bidding process which also saw the 2022 event awarded to Qatar.
In 2014, FIFA cleared Russian authorities of wrongdoing, though western critics continued in the run-up to the tournament to question its safety credentials and suggest it could play into Putin's hands politically. Qatar has also been cleared of wrongdoing.
But last year's month-long event, spread across 11 cities, passed off without major security incidents and was deemed a success by players and fans.
Putin said at the time that the World Cup had helped debunk stereotypes about his country.
Blatter was honoured with state awards by Germany and South Africa, which hosted the 2006 and 2010 tournaments.
(Reporting by Gabrielle Tétrault-Farber; additional reporting by Brian Homewood in Bern; editing by John Stonestreet)
