Global quick service food chain Subway has agreed a sale to US private equity giant Roark Capital in a deal purported to be worth $9.6bn (£7.6bn).

Subway confirmed on Thursday it had “entered into a definitive agreement” to be acquired by affiliates of Roark.

It said the transaction is a major milestone in the previously family-controlled chain’s multi-year transformation journey.

The transaction will combine Subway’s global presence and brand strength with Roark’s expertise in restaurant and franchise business models.

Roark is a private equity firm with $37bn in assets under management, which has focused on investments in consumer and business service companies, with a specialisation in franchise and franchise-like businesses.

Atlanta-based Roark’s portfolio includes Arby’s, the largest drive-thru sandwich chain in the US, bakery chain Cinnabon and Dunkin’ Donuts.

“This transaction reflects Subway’s long-term growth potential, and the substantial value of our brand and our franchisees around the world,” said John Chidsey, CEO of Subway.

“Subway has a bright future with Roark, and we are committed to continuing to focus on a win-win-win approach for our franchisees, our guests and our employees.”

The transaction comes on the heels of Subway announcing its 10th consecutive quarter of positive same store sales.

It will continue to execute its strategy with a focus on sales growth, menu innovation, modernisation of restaurants, overall guest experience improvements, and international expansion.

Subway operates in more than 100 countries through nearly 37,000 restaurants. Subway restaurants are owned and operated by Subway franchisees – a network that includes thousands of dedicated entrepreneurs and small business owners.