From May 1 2015 it will be abolished for passengers aged under 12 and from 2016 for those aged under 16.
Osborne said he wanted to reduce the cost of air tickets for families.
The move may help blunt controversies over the decision by former education secretary Michael Gove to encourage schools to fine parents who take their children on holiday in term time when air fares are cheaper.
The duty is levied at different rates according to the distance a passenger flies and the class of seat they occupy.
It is deeply resented by the airline industry, which welcomed the change.
The Board of Airline Representatives UK's chief executive Dale Keller said: ‘We welcome the chancellor’s announcement which will mean a fairer deal for families.’
He said the move demonstrated ‘the growing awareness within government that the world’s highest air tax needs a severe pruning to boost the UK’s global competitiveness and create more jobs’.
