Dundee City Council said: “Balfour submitted the lowest tender and received the highest quality score for its £28m bid, which includes a commitment to create local employment opportunities.”
The deal is expected to be rubber-stamped by the council next week.
BAM is believed to be the only other bidder to enter the race.
Ken Guild Policy and Resources Committee convener said: “We commissioned a report by project consultants Jacobs to find out why the cost was pushed above our original estimates and it notes that there were a number of complex factors that combined to account for the increase.
“Lack of competition in the marketplace combined with the current risk averse approach to rail related projects were key elements, however the council’s new Capital Plan has identified funding for this vital project to go ahead.
“More than 120 construction jobs per year for the two years of the build; £11.6m of gross added value to the local economy; and knock on benefits to the local supply chain all add up to make the concourse project a key economic driver while it is being built.”
The proposed new station building will occupy the site of the former concourse.
It will have a double height ground floor incorporating a passenger concourse, ticketing facilities, as well as a café/restaurant and retail space.
There are three additional floors above this to accommodate a new mid-market hotel.
If councillors back the move work will start in the autumn and take just over two years.
The city has already been hit by construction cost over runs on its V&A museum job being built by BAM.
The budget has almost doubled on the job from an original £45m to £80m.