KKR, whose retail investments include health and beauty group Alliance Boots and toys chain Toys'R'Us, saw off rival bids from Apax, Bain and TPG.
Earlier this month Pets at Home posted a 6.7 per cent rise in like-for-like sales for the six weeks to 7 January.
KKR said it would continue Pets at Home's rapid growth of recent years, which has seen it expand into grooming and veterinary services as well as opening more stores.
Pets at Home made underlying earnings before interest and other costs of £70m on sales of £404m last year.
The Cheshire-based company employs 4,200.
Pets at Home has been growing since it was bought by Bridgepoint, which has doubled its outlets.
It also operates 54 veterinary centres.
European head of retail for KKR, John Pfeffer said: “We are enthusiastic about the significant further potential for Pets at Home to grow, develop and continue to deliver its unmatched breadth of products, store environment, competitive pricing and customer service.”