More than 600,000 people have flocked to the Edinburgh landmark since the latest phase of a 15-year revamp was completed at the beginning of July.
The Â£14.1 million project saw 40 per cent more space created for objects drawn from the worlds of science, technology, decorative art, fashion and design.
More than 3000 objects were installed in the new galleries, three quarters of which were either on display for the first time in a generation, or for the first time since they were acquired.
Nearly 150 new cutting-edge innovations, interactive features and state-of-the-art displays were added to the attraction.
The transformation of galleries more than 50-years-old, as well as little-used or closed off parts of the Chambers Street building, were carried out over the space of around 18 months after the revamp won the backing of the Heritage Lottery Fund and the Scottish Government.
The surge in visitors means the museum, which was less than 2000 behind Edinburgh Castle in the UK league table of attractions, is almost certain to overtake the historic landmark this year.
The castle has experience an extra 106,000 visitors so far this year - an increase of 13 per cent - according to new figures released today.
However museum director Gordon Rintoul said he expected more than 200,000 extra visitors to have come to the museum by the end of this year, which marked the 150th anniversary of the creation of the original Victorian building.
Dr Rintoul said: “We had just under 1.6 million visitors last year and we’re expecting to be up around 1.8m by the end of this year.
“We’ve now had 600,000 visitors to the site since the new galleries opened, which is 25 per cent up on the equivalent period last year.
“We’re very pleased indeed that the public have voted with the feet to see the new galleries and it’s exactly the kind of response we’ve been planning for.
“I would think the increase we have seen is substantially down to the new galleries.
“We have far more for families who are looking for things to do with children, and our art and design galleries have been particularly popular with adults.
“There was inevitably a bit of a dip in our visitors when our previous galleries closed, but the work we did on our programme elsewhere in the building and on special events did a lot to keep people coming.”
The ten new galleries have been unveiled five years after a huge overhaul of the museum’s great hall, the creation of new underground entrances and new spaces for more than 8000 exhibits.
A final phase of an Â£80 million masterplan for the museum, which is due to be completed by 2018, will see new displays created for Ancient Egypt and East Asian treasures.
By the time they have opened, attention will be turning to the displays in the museum’s modern extension, on the corner of George IV Bridge and Chambers Street, which by then will be around 20 years old.