The development will be an annex to the school for three to 18-year-olds in Ystalyfera.
Built on the site of the former Sandfields Comprehensive, the secondary school will have 650 places.
Education Secretary Kirsty Williams said: "This money will address the region's growing demand for Welsh medium education."
The Welsh Government has awarded £10.69m towards the project as part of the 21st Century Schools programme which aims to update school buildings across Wales.

Fathi Zeidan, nicknamed "Zorro", was the Fatah movement's security chief in the Mieh Mieh Palestinian refugee camp.
There was no immediate claim of responsibility for the blast, which occurred in nearby Ein el-Hilweh camp.
However, Fatah gunmen have recently been involved in clashes with rival factions in Ein el-Hillweh.
One man was killed earlier this month when one dispute escalated.
Lebanese security officials say the bomb that killed Mr Zeidan was placed inside his car and  he would have died instantly.
About 450,000 Palestinians are registered with the UN as refugees in Lebanon, and most live in 12 official camps that mainly fall outside the jurisdiction of the Lebanese security services.
Money for a new £17m Welsh medium school campus in Neath Port Talbot has been approved by the Welsh Government.
[NEXT_CONCEPT]
A local Palestinian official has been killed in a car bomb explosion near the south Lebanese port city of Sidon, Lebanese security officials say.