Schools which find the most effective ways to help children from poor backgrounds could win £10,000, Deputy Prime Nick Clegg has announced.
The awards will be made to 50 schools which make best use of the "pupil premium", a £600 payment given for each child who receives free school meals.
Mr Clegg said this would "reward and celebrate" the improvement in young people's life chances.
But Labour said the premium was being used to "plug holes" in school funding.
The payments - affecting 1.8 million children - will cost a total of £2.5bn a year by 2015.
Mr Clegg said the extra money being announced was not "all about the glitz and glamour of winning prizes", but would help "boost" teachers and the education system in general.
Other proposals he outlined included funding summer schools with £500 for each pupil to bridge the gap between primary and secondary education.
There would also be career incentives for teachers willing to work in schools with large numbers of disadvantaged children.
The pupil premium was one of Mr Clegg's highest-profile policies during the 2010 general election.
In a speech at a north London primary school, he said the Lib Dems had "won the battle" within the coalition over the payments, ensuring they were properly funded.
He said: "Get this right and we make good on education's progressive promise: to give every child the chance to go as far as their abilities and effort can carry them.
"And we'll achieve something else of lasting importance. We'll prove that teachers do best when Whitehall steps out of the way.
"To that end, I want to strike a deal between the coalition government and our schools and teachers: We'll give you the cash; we'll give you the freedom; we'll reward and celebrate your success.
"But in return we want you to redouble your efforts to closing the gap between your poorer pupils and everyone else.
"We won't be telling you what to do, but we will be watching what you achieve."
'Got a nerve'
In a separate interview Mr Clegg told BBC Breakfast: "This is a very big change to the pupil premium. It's money that's being given to schools and teachers.
"They are then entirely free to use that money as they see fit to help children from disadvantaged backgrounds to get a head-start in life that they deserve."
For Labour, shadow education secretary Stephen Twigg said: "Nick Clegg has got a nerve talking about social mobility. His government has cut education spending by the biggest amount since the 1950s.
"More than half of head teachers say they will be forced to use the pupil premium to plug holes in their budget."
Brian Lightman, general secretary of the Association of School and College Leaders, welcomed the positive tone of the speech, but he said the awards would not "have a massive impact on performance".
Christine Blower, general secretary of the National Union of Teachers, said: "Introducing competition for funding amongst our schools is quite unacceptable. All schools must be fully resourced to provide the first class education service we need."
Martin Johnson, deputy general secretary of the Association of Teachers and Lecturers, said: "The coalition government's austerity policies, with its attack on the jobs, pay and conditions and benefits of the less well-off, are increasing the [education] gap.
"The real answer to the achievement gap lies in new economic, industrial and regional policies, not in education policies based on dodgy stats and cheap gimmicks."