Following the sale, the Jane of Newmarket name will disappear after 44 years of trading and the store will be rebranded and refitted as Anne Furbank in late July.
Anne Furbank managing director Rebecca Furbank said: "It was an opportunity we couldn't say no to. We weren't looking for a business as big as that but there is a great team at Jane of Newmarket and we want to nurture it and grow it. Jane has been a great buyer. It has a great database and a great location."
Both stores are Drapers Award winners and stock a similar mix of brands, including Gil Bret, Betty Barclay and Frank Usher. The shops are about 30 miles apart.
Jane of Newmarket owner Jane Webb started the business in 1964. She said she had decided to sell the business because of new buying patterns, which meant she spent most of her time in London.
Anne Furbank was founded 25 years ago in Buckden, Cambridgeshire. The company also runs the George Hotel and Brasserie in nearby St Neots.