Summer temperatures in the Gulf state can reach 50C, sparking health fears for players and fans alike.
Uefa’s 54 member associations backed the switch at a meeting in Croatia.
“The World Cup cannot be played in Qatar in the summer,” said Fifa vice-president Jim Boyce. “Everyone was certainly in agreement about that.”
Boyce, a former president of the Irish Football Association, added that the debate was now whether the tournament would be played in January of 2022 or in November and December of that year.
Uefa favours January so that it does not impact on the Champions League, but British associations want to ensure their domestic festive fixtures are protected.
Boyce says the associations do not want Fifa to rush that decision.
“There is still nine years to go and people feel Fifa should sit down with all the major stakeholders and come up with a solution that would cause the minimum disruption to football,” he said.
“There is plenty of time to do that in my opinion.”
Fifa could agree in principle to alter the timing of the World Cup at a meeting in Zurich early next month, but the news that European football chiefs are backing a switch is significant.
That is because European associations represent 10 members of Fifa’s 22-strong executive committee, which will make the final decision.
Some domestic leagues around the world are likely to be unhappy at Thursday’s news.
The English Premier League declined to comment, but has always opposed a switch and together with other European leagues, has called for there to be no definitive decision next month and a full consultative process.
Chief executive Richard Scudamore said last month that a winter World Cup would be too disruptive and cause major disruption to three domestic seasons – 2021-22 and the ones either side – as well as impacting on broadcasting contracts.