The school, St Cyprian's, has the full backing of the south London borough of Croydon, and will receive funds - and seconded language teachers - from the Greek government.
Its backers have applied for voluntary-aided status and say they will be able to raise more than the 15 per cent funding required. They have already raised Pounds 500,000.
The DFEE has agreed to contribute Pounds 40,000 towards design costs needed to convert a former school building into a three-form entry primary school.
The school day will be extended by 30 or 45 minutes so it can deliver the full national curriculum and teach Greek language and religion.
Antonia Kastelanides, spokeswoman for the Greek Association of Language Enhancement, said: "Independent research shows support for a denominational school in the area and the school will also admit 10 per cent non-Orthodox pupils to ensure a pluralist ethos.
"Most of the children attending will have English as their first language, but may be familiar with the ecclesiastical Greek they hear at church."
The aim is to open the school next September. The DFEE's decision is expected before Christmas.
David Sands, Croydon's director of education, said: "I'm sure the school will be very popular and it has a great deal of public support. We have included the places it would provide in our action plan for reducing infant classes sizes.
"We have kept held the building empty for a year but because of the costs we will not be able to do so indefinitely."
Muslim bid, page 14