The award, the first made by the Big Lottery Fund's Children's Play grants programme, is the largest single sum the bureau has ever received. It will account for a fifth of the charity's budget in the next financial year.
The bureau will use the money to open nine regional offices providing infrastructure support to other organisations, many of them in the voluntary sector, which will deliver a £155m lottery-funded children's play project across England over the next five years.
"This is very significant for the play sector," said Paul Ennals, chief executive of the bureau. "It's taken a long time to convince the Government of the logic of the project, and then we had to persuade the Big Lottery Fund as well."
Children's charities first began lobbying ministers to increase play opportunities in 1998.
"The Government said that, if there was a common message, it would listen," said Ennals. So the Children's Play Council, an alliance of public and voluntary sector organisations promoting play, which is led by the bureau, started pressing for action.
In 2001, the Department for Culture, Media and Sport asked the council to develop plans for a project. After formulating proposals, the play council submitted a lottery bid in December.
Ennals has pledged that the regional offices will be open for business by the end of March. The offices will support organisations delivering the Play England Project across England.
A total of £155m has been earmarked for the project, of which the lion's share - £124m - will go to local authorities. Although only councils can submit bids, charities are expected to deliver the majority of the schemes. The bureau's £15m will go on supporting the schemes and a further £16m, as yet unallocated, will go towards promoting innovation.
Ennals does not think the grant was an example of the Government raiding lottery coffers for its own purposes. "We understand there is an issue about the lottery's independence," he said. "But it looked at the evidence available and consulted before making its decision."
A spokeswoman for the BLF said: "We have not replaced any mainstream funding. In our consultation, we found play is something people want us to support."