BAM Construction will now start work on the flagship building at the city’s waterfront next month.
The deal comes after the council dropped the bombshell last month that the project’s price tag had almost doubled from the original estimate of £45m.
But by the time BAM Construction was named preferred bidder last September it was known the ambitious price target was too low.
The council has now won further financial support from the Scottish government and Heritage Lottery Fund to bridge the budget gap.
Doug Keillor, Regional Director of BAM Construction in Scotland said: “This is the most unique construction project that my team have ever been involved in, both in architectural vision and in the way it will be built.
“It’s challenging, but in a good way. Watching it take shape over the next few years using a combination of local, national and international expertise, will be very satisfying.”
The building project will also bring considerable attention to Dundee as the vision of architect Kengo Kuma takes shape before opening to the public before June 2018..
Dundee City Council administration leader Councillor Ken Guild said: “This project will help to attract further investment into the city and we are already experiencing unprecedented levels of investor interest in Dundee.
“Construction of V&A Dundee will give our economy a significant boost and help to create hundreds of jobs.