The new school is due to open in September 2018, with post 16 education provided at Ysgol y Preseli 20 miles (32km) away.
It comes despite concerns from Ysgol y Preseli's governing body, which said the Crymych school could lose 300 pupils.
It also warned of "significant" staff redundancies at the school.
In a letter to the council's director for children and schools, Ysgol y Preseli's chair of governors, Des Davies, warned the school could "lose up to 300 pupils from the school between 2018 and 2023", which would mean a reduction of Â£1.25m in funding over five years.
He added this "will unavoidably lead to the redundancies of significant numbers of staff".
Mr Davies called for the need to reconsider catchments for the two schools and an opportunity to "discuss further which catchment particular schools belong to, for example Tenby and Narberth".
But Councillor David Lloyd, the council's newly appointed cabinet member for education, said Ysgol y Preseli's concerns would be "dealt with sensitively".
In a report to the full council, officials say that the authority's Welsh in Education Strategic Plan offers a clear vision for developing and extending Welsh medium education.
They also say that parents at Ysgol Hafan y Mor (Tenby) and Narberth CP School with be able to choose whether to send their children to the new school or Ysgol y Preseli between September 2018 and September 2022.
The full council's decision means Ysgol Gymraeg Glan Cleddau in Haverfordwest will be discontinued.
The future of primary education in Milford Haven was also on the agenda on Thursday.
Councillors supported a recommendation to start a statutory consultation on plans to close The Meads Infant and Nursery School and Milford Haven Junior School and build a new 3-11 school using both the current school sites.
It aims to address "significant levels of overcrowding".
Surplus places at the nearby St Francis CP School would be addressed by extending the age range in order to admit part-time and three-year-old pupils.
Pembrokeshire council is to press ahead with plans to open a new 3-16 Welsh medium school in Haverfordwest.