The west-London school graded outstanding was set up by a group of teachers in 2012 and is one of more than 300 free schools that have opened since 2010.
The newly approved free schools will now start to confirm sites with many of them expected to open in September 2017, the Government said.
They are the first free schools to be approved under a new fast-track process with many of them set up by existing schools or multi-academy trusts.
The Prime Minister said that free schools had been ‘at the heart of this Government’s education reforms’.
There are now 304 more free schools and 5,188 more academies than in 2010.
The Conservative Party’s pledge to open 500 new free schools in this Parliament was a key manifesto commitment.
Mr Cameron said, ‘More than 300 have been created since I became Prime Minister and 200 are set to open meaning tens of thousands more young people, many from disadvantaged areas, finally have a choice of a good education that helps them to reach their full potential.
‘I am proud of what this Government has achieved, working with heads and teachers to raise standards so that our young people have the best possible start in life.’
Reach Academy was the first all-through free school to be awarded an outstanding grade in March 2014.
A second Reach Academy is one of the 31 new free schools approved and will open in Hounslow. Reach Academy 2 takes its inspiration from the Harlem Children’s Zone (HCZ) in New York City.
The new school will replicate HCZ’s focus on early intervention with two- and three-year-olds. Strong relationships with families will be developed through home visits and integrated family support.
Another approved school is the Avenue in north-west London, which will cater for children with Autistic Spectrum disorder and complex needs and is being set up by the Brent specialist Academy Trust, which runs three special schools.