It is one of 35 projects throughout the UK which will share a total of pounds 52m awarded by the Heritage Lottery Fund.
The museum's high-tech new wing, due to open in 2000, is the most significant development at the site for 30 years.
Work will start on the pounds 44m extension in the autumn. It will include four floors of exhibition space, London's first Imax (big screen) film theatre, a scientific garden and interactive displays.
The first major award of lottery cash towards the sciences coincides with National Museums Week.
Research confirms that the Science Museum is one of Britain's fastest- growing attractions and has received more school visitors than any other venue in Britain.
However, in an attempt to ward off criticism that London has received the biggest slice of the lottery cake, a spokesman emphasised that 68 per cent of last year's school visitors came from outside the capital.
Virginia Bottomley, the Secretary of State for National Heritage, described the Science Museum award as "an excellent example of how lottery money can be used to invest in our future generations".
The Museum of Worcester Porcelain, in Worcester, also received just over pounds 1m to redisplay its collection in a new extension, and the Inner Hebridean island of Mull was awarded funds to create a visitor centre at Iona Abbey.
The Heritage Lottery Fund also gave a pounds 1.65m grant to help the Scottish National Portrait Gallery buy an oil painting by the Flemish artist Van Dyck - a study of Charles I's two daughters, Elizabeth and Anne, done in preparation for a larger group portrait which hangs in Windsor Castle.
The pounds 2.2m study, painted from life in 1637, shows Elizabeth cradling her baby sister to her breast. Neither princess lived past childhood.
The gallery's keeper, Dr Duncan Thomson, said it was unusual for Van Dyck to make an oil study for a major work instead of drawings.
"It brings the past immediately to life, so that you can virtually hear the children breathe and hear Van Dyck's brush recording the likenesses of the children on his canvas.
"No doubt they moved a lot, so he had to work with great speed. But he had an eye and a hand that could accomplish such things."