A Fifa taskforce recommended last month that the tournament should be switched from summer to winter.
The decision to hold the final on 18 December means Britain's traditional Boxing Day club matches on 26 December can still take place.
In another key decision, Fifa has chosen France to host the 2019 women's World Cup ahead of South Korea.
France will also host the Under-20 women's tournament in 2018.
Confirming the date for the 2022 World Cup final, Walter De Gregorio, Fifa's director of communications, said: "This is for us an important step.
"Finally we know the end of the tournament. It's a Sunday and, by the way, it's the national day in Qatar, so it fits perfectly."
He added: "You have enough time to do your Christmas shopping."
The decision to move the 2022 World Cup from its traditional June and July slot was taken because of health concerns for players.
Summer temperatures in Qatar can exceed 40C.
Fifa has also indicated that the 2022 World Cup could be shortened to 28 days. It normally lasts for 31 or 32 days.
Uefa, the body that governs European football, had pushed for the final to be as late as 23 December.
However, that option attracted opposition from Fifa members, who feared it would cause problems for fans and players getting home in time for Christmas, as well as affecting club football's festive programme.