The landmark was notched up by a German youngster just over 500 days since the museum was unveiled.
It was announced weeks after official research revealed that the V&A, which cost £80 million to build, had generated £75 million for the Scottish economy in its first year of operation.
The city’s waterfront museum - which is said to have supporting the equivalent of 2143 full-time jobs across Scotland - has become one of the country’s busiest visitor attractions since it was unveiled in September 2018. More than 624,000 visitors were attracted to V&A during 2019.
Although full visitor attraction numbers are yet to be revealed, the V&A could outstrip the Royal Yacht Britannia in Leith, Culzean Castle, in Ayrshire, and the Glenfinnan Monument in the Highlands.
One in three of its visitors have been drawn from Dundee and the wider Tayside area, with 42 per cent from the rest of Scotland, 14 per cent from the rest of the UK and 10 per cent from overseas.
V&A Dundee attracted more than 300,000 visitors in its first three months and 830,000 in its first 12 year. It was predicted that it would attract half a million visitors in its first year.
The museum, designed by award-winning Japanese architect Kengo Kuma, has secured worldwide publicity for Dundee since the building, the centrepiece of the city’s £1 billion waterfront regeneration, began to take shape after work got underway in 2015.
The arrival of the V&A in Dundee is already thought to have boosted the value of tourism to the local economy to a record £187 million - up 8.7 per cent in the space of 12 months.
Seven-year-old Nalani Becker, from Berlin, who was visiting the museum with her father Jan, became its millionth visitor yesterday.
V&A Dundee director Philip Long said: “I'm thrilled that we've welcomed our one millionth visitor, just over 500 days after opening the doors of Scotland’s first design museum.
“We have a hugely exciting year ahead, with the last chance to see our UK-exclusive exhibition Hello, Robot this weekend and our first major fashion exhibition on Mary Quant opening in April.
"I'd like to thank everyone who has helped to create V&A Dundee and who continues to support its incredible success."
Dundee City Council leader John Alexander said: "This is another tremendous achievement for V&A Dundee and the city.
“Our stunning museum is now very firmly part of the cultural fabric of Dundee, with its design galleries and exhibition programme attracting locals and visitors alike.
“It has raised Dundee’s international profile and played a key part in securing record-breaking tourism figures. V&A Dundee is helping to create jobs and new economic opportunities for the city.”
Caroline Warburton, regional leadership director at national tourism agency VisitScotland, said: “The economic and cultural impact of V&A Dundee on the city and its surrounding area can’t be overestimated.
"Since its opening, it has drawn the eyes of the world, and visitors alike, to Dundee and has been a great catalyst for collaboration across the tourism sector in Tayside.
"Achieving a million visitors in just over a year is a testament to the quality of the world-class experience the attraction offers.”
Scottish culture secretary Fiona Hyslop said: “I’d like to congratulate V&A Dundee for welcoming its 1 millionth visitor, an impressive achievement and a sign of the museum’s strong appeal to visitors from around the world.
“The museum, built with the help of £38 million in Scottish Government funding, has already more than proved its cultural value, far exceeding expectations for visitor numbers and improving Scotland’s status as a prime destination for world-class cultural experiences.”
UK arts minister Helen Whately said: "In a short space of time V&A Dundee has had a huge impact: bringing millions to the Scottish economy, championing Scottish design and now celebrating its millionth visitor.
"The museum has become a tourist magnet, delivering huge benefits to Dundee and the surrounding area, and the UK Government is very proud to be one of its early backers."
KEY FACTS AND FIGURES
120: Entries to the international design contest won by Japanese architect Kengo Kuma in 2010.
£80.1 million: The total cost of design, construction and fit-out of V&A Dundee.
2429: The individual concrete panels fitted on the outside of the building.
£75 million: Estimated impact of V&A Dundee across Scotland..
696: Number of full-time jobs supported in Dundee.
2143: Number of full-time jobs supported across Scotland.
£32 million: Spending from V&A Dundee visitors in other businesses in the city.
370: Additional jobs believed to have been created in Dundee since the V&A opened.
500,000: Expected visitor numbers for first year of operation.
830,000: Actual visitor numbers for first year.
£187 million: Current estimated annual value of tourism to Dundee.
3033: Number of full-time jobs in Dundee which are supported by the tourism industry.