The company currently employs 500 people at premises in Glasgow, Robroyston, Livingston, Ayr, Clarkston, Hamilton, Lanark and Clydebank.
The expansion plans include new stores in Port Glasgow and Irvine, while other locations are "in negotiation".
Existing stores in Clarkston, Ayr and Livingston will also be enlarged.
The family-owned business, which is currently celebrating its centenary, has forecast a turnover of between Â£25m and Â£30m in 2015.
Its sells a wide range of products, including clothing and accessories, housewares, jewellery, watches, books, toys and confectionery.
Owner Willie Watt said: "Our business has changed dramatically since it first opened its doors in Glasgow's Sauchiehall Street, when the focus was exclusively on high-end ladies' fashions.
"We have evolved as a business and recognised that a retail offer including a wider range of great value products in a department store-style setting has greater appeal to today's consumer.
"We've seen positive growth in terms of both turnover and customer numbers, even in the recent recessionary period, and we've continued our expansion in terms of new store openings.
"My long-term plan is to have a total of 16 stores throughout Scotland, and we're constantly looking at new opportunities to secure ideal locations."
Retailer Watt Brothers has announced plans to create 350 new jobs by opening six new stores and expanding three others over the next few years.