The Asda store, which will have a 40,000sq ft gross floor area, is being built on a redundant site behind the former health centre, which Barr Construction has just started demolishing.
Barr will also deliver 250 spaces for car parking, much of it below the raised supermarket building, and a petrol station.
The building contract is thought to be worth around £10m and saw the firm beat rivals ISG, Gilbert Ash and Robertson Group.
Derek Simpson, Operations Manager for Barr Construction, said: “This is our second project with Asda following the opening of the Dundee store earlier this year, we are looking forward to continuing our relationship with the retailer.”
The work is part of two major multi-million-pound regeneration projects that will change the face of Barrhead Main Street.
East Renfrewshire Council’s Convener for infrastructure and sustainable growth, Councillor Tony Buchanan, said: “We are delighted to get work under way on our substantial investment programme in Barrhead, the Foundry.
“This will be a fantastic addition to Barrhead and will really transform the Main Street.”