The €122m (£110m) contract also includes the construction of a rescue and fire station, a hangar and several service and administration buildings.
The project involves the excavation of more than 1.5 million cubic metres of material and will require 247,000t of asphalt mixture and 58,000m³ of concrete to be placed.
Strabag holds a 53.92% share in the contract, which is due for completion by the autumn of 2019.
“The beautiful historic old town of Dubrovnik is a major tourist attraction. Dubrovnik Airport plays a crucial role in providing access to the city and its expansion is an important investment to help cover the rising demand for capacities in the future,” said Thomas Birtel, CEO of Strabag SE.