Hornby will replace Andy McCue, who announced in February that he was leaving the company due to "extenuating personal circumstances", having joined the group from Paddy Power in September 2016. At the end of last year McCue oversaw the completion of the acquisition of Wagamama for £559m.
Hornby will join the Restaurant Group from his current role as co-chief operating office as betting company GVC Holdings. He was previously chief executive of Coral, chief operating officer of Gala Coral and chief operating office of Ladbroke Coral (following the merger with Ladbrokes in 2016).
Earlier in his career, Hornby headed up HBOS as chief executive before going on to be group chief executive of Alliance Boots.
Hornby's salary will be £630,000 with no pension, but with a maximum annual bonus of 150% of his salary.
He said that he was "delighted" to be joining the Restaurant Group at such an exciting time. "This is a great business, with strong brands, committed colleagues and tremendous potential to grow. I recognise that this sector of the market faces considerable challenges, but the Restaurant Group has a set of casual dining and pub brands that offer significant potential. I'm excited to have the opportunity to lead the team and look forward to getting out and meeting colleagues when I join."
Debbie Hewitt, chairman of the Restaurant Group, added: "Andy's extensive retail background, proven hands-on operational expertise, and experience of integrating businesses position him well to provide the leadership required to deliver the next phase of our strategy."
The Restaurant Group's like-for-like sales dropped by 2% last year, with total sales up to £686m. In April it was revealed that the company had put 44 sites up for sale, half of which had ceased trading.