The money will be used to refurbish the RADA building in Bloomsbury, central London, to buy two neighbouring properties and put the latest theatre technology into the RADA theatre where students demonstrate their talents to the paying public and to agents seeking future stars.
The list of graduates is a roll-call of the biggest names in acting. It includes Lord (Richard) Attenborough - who is now chairman of RADA - Sir John Gielgud, Penelope Keith, Glenda Jackson, Albert Finney, Peter O'Toole and Kenneth Branagh.
The institution has not generally been thought of as one in urgent need of cash; and its facilities and teaching standards have continued to be sufficient to recruit and produce the leading talents of successive generations.
But the principal of RADA, Nicholas Barter, said the academy "desperately needed" to upgrade its facilities. It has been at the same site since it was founded in 1904. "RADA was hit by a bomb in 1942 and has never really had the funds to recover itself," he said.
"Our students have lived in very bad conditions for years. The lottery cash is a tremendous boost."
Mr Barter said any accusations that the grant was a windfall for "luvvies" would be misplaced. "We're drawing people in from all over the country - we hold auditions in Manchester, Nottingham, Newcastle and Belfast.
"It's not in any way an inwards-looking institution, we're drawing new blood into the theatre and we're looking for people from homes across the social spectrum.
"You'll find as many regional accents at RADA as you find on television. "We're a British institution and an international one - our short courses attract people from 14 different countries."
The academy, which charges students pounds 6,930 a year and receives no government funding, won an pounds 850,000 lottery grant last summer to design and plan the major project.
Lord Gowrie, chairman of the Arts Council of England, said: "RADA has a world-wide reputation for the quality of the performers and stage technicians it trains.
"The Arts Council is delighted to support, through a lottery award, the refurbishment and renovation of the buildings.
"Significant improvements to both the teaching facilities and the performance spaces will ensure that succeeding generations of actors and actresses remain at the top of the world league like the present generation."
RADA has 30 places available each September, even though some students must pay their own hefty tuition fees - more than pounds 20,000 over three years.
The number and amount of discretionary grants from local authorities have been cut in recent years.
Students train from 10am to 6pm each day, and may have individual classes or performances in the evening.
Lord Attenborough said he was "thrilled and delighted" at the good news. "We have already raised pounds 2m privately towards our required partnership funding and need to raise a further pounds 6m over the next three years.
"These major sums of money will be devoted to the training of young people from all over the United Kingdom. Each has the potential to become one of the stars of tomorrow."
The trainees were selected purely on merit and drawn from every walk of life, he said. "The vast majority cannot afford to live in London and pay for their tuition.
"Unfairly, most of them are also unable to obtain grants from their local education authorities - unlike fine arts, music and university students who qualify automatically."
RADA was setting up a scholarship fund so that no outstanding talent would ever be turned away, he said.
The Serpentine Gallery, in London, chaired by the former Arts Council chairman Lord Palumbo, also received a lottery award yesterday. It got pounds 3m from the Arts Council to help fund a refurbishment programme to improve visitor facilities, disabled access, air-conditioning, security and behind- the-scenes accommodation.
A time of parties, vowels and accents
ALBERT FINNEY (above)
I felt awkward, clumsy, unattractive and incapable of showing anyone a good time, since I couldn't even buy my way into their favours. I didn't feel that I was a find at all.
I were done for ABH when I were a student there. Me and a mate were looking for a party one Friday night. Someone tried to shut the door on me and I ended up whacking him a couple of times. I got fined pounds 50.
It was a bit like a finishing school then, full of rich aristocrats. I spent the whole time with a bone prop in my mouth to open my vowels. I was made to feel very inadequate.
You were prepared for classical work and so you were expected to speak with a middle class voice. I was on a scholarship and I had to do whatever I was told so I got rid of the accent.
JANE HORROCKS (below)
RADA was brill. Drama school is cushy, you get a grant, you try out a good range of parts, but then suddenly you are thrown out to sink or swim.