Unite's national officers, Brian Boyd and Brendan Gold, said: "Unite came to these negotiations with a strong mandate for industrial action.
"Today's negotiations between Unite and BAA – with the assistance of Acas – have been constructive and Unite is pleased to announce it is calling off the strike action at BAA's six airports.
"Unite's negotiating committee will recommend a much improved offer from BAA. Details of the agreement will be made public once BAA staff have been advised of the improved offer.
"We would like to particularly thank Acas for its valued assistance through these tough negotiations."
The union will now ballot its members on the details of the offer.
Peter Harwood, Acas chief conciliator, added: "As you would expect the details of the deal are confidential until the parties report back to their respective constituencies. We understand that this process should be completed by 1pm tomorrow after which details will be disclosed.
"The unions will now be balloting their members on the proposed settlement with a recommendation that members vote to accept it.
"Acas is pleased at this development and hope that the matter will soon be settled."
