Conygar Investment Company PLC wants to build on the Old Brickworks site at Tremarl Industrial Estate, Llandudno Junction.
The company has previously said 300 jobs could be created.
Councillor Nigel Smith described the plans for the 6.5ha (16 acre) site as "fantastic".
Tesco, which has a major store at Llandudno Junction, and Mostyn Estates, ground landlords of most of Llandudno, had objected to the plan.
A new £40m supermarket and restaurant development in Conwy county has been approved by councillors, despite objections.