The island public services department will now enter a three-month value engineering phase to work out detailed plans and costs for the runway project, which has been budgeted at £81m.
The Belfast firm was selected as preferred bidder, based on quality of submission, price, and proposed use of local labour.
In the last decade Lagan has built up a track record of 35 airport projects worldwide.
Work on Guernsey airport is expected to begin in August and will take around two years to complete.
It involves the reconstruction of the runway and other hard surfaces, and the replacement or refurbishment of the drainage system, airfield lighting and other key operational systems.
The current airfield boundary will also be extended to the west to provide longer grass runway end safety areas to protect passengers and aircraft in the event of an ‘overshoot’ or ‘undershoot’.
Public Services Minister Deputy Bernard Flouquet said: “The urgent repair of the runway is only one aspect of the work required, and represents only around a third of the budget.
“We are also installing a completely new drainage system, replacing the concrete apron areas, installing new ground lighting and upgrading other key systems.”
He added: “It is therefore essential that we appoint a lead contractor with the relevant expertise, and in Lagan Construction we have one of the most experienced airfield construction companies.’
Once the construction phase begins, work on the runway will primarily be carried out at night, while the airport is closed, and will be reinstated prior to reopening at 6am each morning. That element of the project is expected to last around seven months.
Measures will be in place to minimise disruption from the works at night.
This will include best practice procedures on the handling of materials and operation of equipment, and fencing to reduce noise and light impacts.
The reconstruction of the concrete apron areas, where aircraft park while passengers board and disembark, will be carried out in phases. That work will take place during the day, while the airport remains operational.