Hornby replaces Andy McCue in the position, who will step down on 30 June. The company will led by Debbie Hewitt through the interim period.
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 officer 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.