More than 3,000 objects are now being installed into four galleries of decorative art, fashion and design and six of science and technology.
The new galleries represent the next phase of the £80m masterplan to transform the museum.
They will be completed in the 150th anniversary year of the Victorian building, which first opened in 1866.
Display space will increase by more than 40%, with 75% of the objects on display not having been seen for at least a generation.
The £14.1m project is supported by the Heritage Lottery Fund, the Wellcome Trust and the Scottish government, with £7m of the costs being raised from trusts, foundations and individual donors.
Alongside the announcement of the opening date, National Museums Scotland launched the last phase of its fundraising appeal for the new galleries.
Edinburgh author, Alexander McCall Smith, who is a patron and long-term supporter of National Museums Scotland, said: "I love to write about Edinburgh.
"It is one of the great cities in the world - rich in history, architecture and culture.
"And the National Museum of Scotland, situated in the heart of Edinburgh, is a place which connects Scotland to the world and the world to Scotland through stories captured in thousands of remarkable objects.
"It's a place which has inspired me and, with the help and generosity of the public, can inspire many more people in years to come."
Gordon Rintoul, director of National Museums Scotland said: "We are now in the final phase of work as we progress towards opening our new galleries on 8 July.
"From Dunlop's first pneumatic tyre to cutting edge scientific discoveries from CERN, the fashion of Vivienne Westwood and Alexander McQueen, Dolly the Sheep and Picasso ceramics - we have something to appeal to everyone."
Ten new galleries at the National Museum of Scotland are to open on 8 July 2016, officials have revealed.