According to the agreement, which was reached with UCATT, the GMB and the T&G, all site employees will finish work on a Friday lunchtime after a five-hour day.
Workers who have to travel long distances to see their families will then be able to take cut-rate flights. It is understood that these will be provided by BA.
The deal averts the threat of industrial unrest at the £3.7bn airport extension.
This arose after workers complained that travel arrangements and bonus payments were falling short of what had been agreed before the project started.
A Laing O'Rourke statement said: "The company has negotiated on behalf of the employees discount air fares for those wishing to fly to selected locations in the UK."
The statement added that there would be a three-monthly review of bonus payments.
The company has negotiated discount air fares for those wishing to fly home
George Brumwell, the general secretary of UCATT, said the deal was the best in the British construction industry. He said: "We have reached agreement and everybody is signed up to the deal."
Laing O'Rourke this week released details of other services that it intends to provide for T5 workers.
The company said that it planned to open a convenience store later this month and to publish a newspaper to keep site workers informed about developments on the project.
The contractor also plans to open other stores selling kit and clothing and to introduce buses to make journeys to work more comfortable.
It is understood that the company is looking to recruit a human resources manager to help oversee industrial relations on its projects.