The outgoing chief executive has been at the helm for eight years and oversaw two private equity takeovers, the most recent a £955m acquisition by KKR.
The firm has grown exponentially under his leadership, reporting profit growth of more than 10 per cent last year to hit £93m, on sales of £518m.
Davies says he told the board at the start of the year that he would leave to seek new challenges.
Davies said: “My time at Pets at Home has been hugely rewarding and enjoyable and it has been a great pleasure to manage such a special business and work with such talented and passionate people.
“The calibre of the team leaves me in no doubt that the business will continue to go from strength to strength through its next phase of growth.”
Tony DeNunzio, chairman of Pets at Home, said: “KKR and I would like to thank Matt for his contribution to the company over the past ten years. He has helped build an excellent business, with a very strong management team and an exciting growth strategy. He has been a pleasure to work with.”
Pets at Home was bought by Bridgepoint from its founder Anthony Preston for £230m in 2004.
DeNunzio says the company is in the process of looking for a replacement. Pets at Home employs more than 5,000 people across its retail outlets and veterinary clinics.