Culture minister Michael Russell said the project could create up to 900 jobs and add £5.7 million to the Scottish economy.
It is intended to show collections from the main museum in London, display Scottish applied arts and design and be large enough to attract international touring exhibitions.
Russell said: "This government has given the V&A at Dundee project team a significant commitment of support which will enable them to move forward and maximise their fundraising campaign.
"We will contribute capital funding towards construction of the physical space and the exact support level will be confirmed once we are in a position to set budgets for the next two to three years."
Professor Pete Downes, chair of the V&A at Dundee project steering group, said it was conducting appraisals of potential sites on Dundee's waterfront.