The West Somerset Council-run facility closed in 2008 after attempts to find a buyer for the pool failed.
A meeting of the council's planning committee voted to approve Lidl's blueprint for the 2,264 sq m site with 100 parking spaces.
The supermarket said the single-storey Seaward Way complex would provide up to 32 new jobs for the town.
Those against had argued the town "did not need another supermarket" and the Lidl store would have a "significant adverse impact" on other shops in the area.
At present the site is a mix of hard standing and grassed areas.
Previously it had been used as a temporary coach park.
Also approved at Thursday night's meeting were plans for eight semi-detached homes and nine "affordable" flats at Ellicombe Meadow, Minehead.
Plans for a supermarket on the site of the former Aquasplash pool in Minehead have been given the go-ahead.