The new competition is expected to include eight teams from Europe.
It will run every four years and take place from June to July in the slot currently used for the World Cup warm-up event, the Confederations Cup.
“Now the world will see a real Club World Cup where fans will see the best teams in the world compete to be crowned the real world champions,” he said.
As well as eight European clubs, the new tournament would see six teams from South America, three each from Africa, Asia and North and Central America and one from Oceania.
It has been suggested each club could earn £50m from taking part.
The European Club Association (ECA) says any new competitions should be part of an agreed framework for the international match calendar post-2024.
ECA board members, including Manchester United’s chief executive Ed Woodward, signed a letter expressing concerns, which was revealed earlier on Friday.
“[We are] firmly against any potential approval of a revised CWC – no ECA clubs would take part,” it said.
When asked if he was concerned about staging a new Club World Cup without any of Europe’s elite clubs, Infantino said: “We hope that all the best teams will participate and we’ve had some very positive discussions with Uefa.
“But it was our responsibility to take a decision because we have to deal with the organisational matters – it is only two years away.”
The Fifa Council also decided that it would be “feasible” to expand the Qatar 2022 World Cup from 32 to 48 teams.
World football’s governing body voted to expand the 2026 World Cup – which will be hosted by Canada, Mexico and the United States – to 48 teams in 2017.
The council will now discuss potential additional hosts to Qatar and a final decision will be made at a Fifa congress in Paris in June.
“If it happens, fantastic. If it doesn’t happen, fantastic also,” said Infantino.
The ECA’s letter was addressed to Uefa president Aleksander Ceferin, who has been asked to explain the position at the Fifa Council meeting, which is taking place in Miami.
The letter, obtained by BBC Sport, stated that there should be no changes to the current fixed international match calendar (IMC), which runs until 2024, and raised concerns about fixture congestion.
It said: “We wish to restate the position of ECA: (a) ECA is unwilling to consider any new or significantly revised competition prior to a holistic assessment of the IMC post-2024 being conducted and an agreement as to its underlying principles being reached; and (b) in any event, a Club World Cup in June 2021, as proposed by Fifa, is not acceptable in light of the existing competitions and the IMC, which is fixed until 2024.”
According to a Fifa document seen by Associated Press, it has been proposed the tournament would run from 17 June to 4 July, with 2022 World Cup qualifiers (31 May to 8 June) preceding it and the African Cup of Nations and Concacaf Gold Cup possibly taking place from 5 July to 31 July.
Fifa said it was aware of concerns of “serious interference with critical matches” but added that members of its own task force “felt that it was feasible to play the Club World Cup” during that period.