It said earlier the value of the deal was 3.0 billion euro ($3.78 billion).
Under the contract, whose signing was long delayed by problems with land expropriation, the Republic's government grants Strabag a 30-year concession to build some 430 kilometres of motorways and high-speed roads, it said in a statement posted on its website.
The Serb Republic is one of the two autonomous parts forming war-divided Bosnia. The other is the Muslim-Croat Federation.
"This is a capital project for the Serb Republic, which will significantly change its image [...], make possible the improvement of communications and create conditions for economic development,” the Serb Republic Prime Minister Milorad Dodik said in the statement.
The government in Banja Luka and the Austrian company will form a 10/90 joint venture company to implement the project, government officials said earlier. The construction of network of roads in the Serb Republic will be one of the biggest investments in Bosnia after the 1992-95 war in the country.
The road network will include a motorway connecting the Serb Republic's administrative centre of Banja Luka with Gradiska at the border with Croatia to the north and an east-to-west motorway from the border with Serbia to the western Bosnian town of Prijedor.
The project also envisages the construction of a section of EU-defined north-to-south transport corridor Vc, connecting the Hungarian capital Budapest with the Croatian Adriatic port of Ploce via Bosnian territory. The Serb Republic government has said the project could be expected to be completed in 2013.
($ = 0.794 euro)