Air passenger duty (APD) for children under the age of 12 on economy travel will be abolished from May 2015, Chancellor George Osborne has said in his Autumn Statement.
From the following year, APD for children under 16 will also be abolished, he said.
Critics said the move inflicted "a fatal blow" to the tax.
The measure follows an announcement in the Budget in March to scrap two APD tax bands.
Air passenger duty is charged on all passenger flights from UK airports. The rate of tax varies according to where the passenger is going, and the class of travel.
"This will save a family of four £26 on a flight to Europe, and £142 on one to the US," the Treasury tweeted.
The move will cost the Treasury £40m in 2015-16. The cost will jump to £80m the following year, and rise to £95m in 2019-20.
'Early stocking filler'
Easyjet said that it would "proactively refund" passengers who have already bought tickets to fly after April 2015.
The British Air Transport Association (BATA) said the government move was "an early stocking filler for families", but it "presents significant practical difficulties" for airlines.
"The industry has always said that changes to APD should have at least a 12-month lead in time due to advance bookings," said BATA chief executive Nathan Stower.
Mr Stower noted proposals to devolve APD powers to Scotland, and called for the tax to be put "out of its misery".
Mark Littlewood, director general at the Institute of Economic Affairs, said the move "not only increases tax complexity, but inflicts a fatal blow to the justification for the tax existing at all".