The consortium offered a price of EUR 2.77 billion for the job.
This is the most valuable project in the Montenegrin history, the government in Podgorica stated on Wednesday.
The 169-kilometre long motorway will go from the seaport of Bar to Boljare on the Montenegrin-Serbian border, and will include 42 tunnels and 92 bridges and viaducts.
According to Lompar, the construction will begin in six months' time at the latest.
The Croatian consortium landed the job in the tender in which bids were submitted also by an Austrian consortium led by the Alpine Bau company, a Greek-Israeli consortium and the Austrian Strabag company.
The Konstruktor director-general, Zeljko Zderic, said it was a big venture in which his company would demonstrate its know-how.