The union said industrial action had been adjourned after talks with BA, chaired by conciliation service Acas, had led to a revised deal for its members.
More than 2,700 of the airline’s Mixed Fleet staff had been due to take part in a two-day walkout in a row over pay and working conditions.
Unite said the new offer would now be put to members through a ballot.
It said the basis for industrial action was as a result of the 4,500 BA workers employed on Mixed Fleet contracts who joined the airline since 2010 being paid less than other staff.
BA said it welcomed suspension of the planned strike action.
Len McCluskey, Unite general secretary said: "We now have a new offer from the company which we will put to our members. The two-day strike over Christmas and Boxing Day is now suspended."
"It will be for our members now to decide if British Airways has done enough to meet their concerns."
McCluskey told BBC News that "Innocent members of the public always suffer when there’s a dispute.
"Any dispute is only brought about because there is a failure between management and the industrial relations within that company."
Unite had claimed that despite earnings for Mixed Fleet staff being advertised between £21,000 and £25,000, in reality, yearly wages began at just over £12,000 - plus £3 an hour flying pay.
The union said it believed at least half of Mixed Fleet employees had taken on second jobs to supplement their earnings, with some cabin crew admitting to sleeping in their cars between shifts as they could not afford the petrol to get home.
