Hewitt, currently non-executive director of Moss Bros Group, will take over her new role on 12 May 2016, following Jackson's retirement.
Jackson, who has given six months' notice of his resignation from his role as chairman from 28 February 2016, will be paid his salary and benefits for the balance of his six month notice period, amounting to a total of £117,000.
He said that Hewitt has "strong business credentials" and will provide "insight and guidance" to the board. "The Restaurant Group has been on a tremendous journey and it has been a privilege to be a part of its growth and development. It is a fantastic company and I have a very high regard for the team. I wish everyone involved in the business every success in the future."
Hewitt added: "The Restaurant Group has great brands and highly talented people and Alan has played an important role in bringing strategic vision, strong market insight and leadership of the board throughout his tenure as chairman. He has taken a proactive role in preparing the board for his succession. I look forward to working with the management team to deliver the next phase of the company's growth."
The Restaurant Group operates over 500 restaurants and pub restaurants throughout the UK. As well as its Frankie & Benny's and Chiquito brands, it also operates Coast to Coast, a pub restaurant business and a concessions business which mainly trades in UK airports.