It will provide space for 300 pupils.
The school will take an extra 30 pupils in September this year and 30 more in 2020. The increased intake will eventually lead to pupil numbers growing by an extra 300 overall – 60 more in each year from 7 to 11.
Councillors were told the growth in predicted demand for places was being fuelled by new homes including at the White Rock development, with more planned for sites along the ring-road in the Paignton area.
There will also be a predicted shortage of secondary places in Brixham next year and Torquay the year after.
A report said the cost of the Paignton Academy scheme worked out at £6,130 per pupil, well below Government guidance of £14,000 to £16,000, and was “excellent value for money”.
Councillors voted unanimously in favour of the £1.84m project, and local members welcomed the investment for Paignton.
Cllr Chris Lewis, Conservative, Preston, said: “This shows a clear message to Paignton parents that we support them, and we support the academy.”
Cllr Dave Thomas, leader of the Conservative group, Blatchcombe, said: “It’s a good news story for Paignton.”
Councillors were told the authority had already allocated £730,000 Government cash towards the project for 2020/21.
They agreed a funding plan for the rest, depending on how much money the Department for Education gives Torbay in its Basic Need grant for 2021/22.
Paignton Community and Sports Academy has around 1,330 pupils aged 11 to 18 and was rated Good after its last Ofsted inspection in November 2016.