Petspiration Group also owns the ecommerce platform Pet.co.nz, has a 2.4 million member loyalty program, and an own-brand range including Caribu and Glow.
Woolworths chief executive Brad Banducci said the 70 per cent of all families in Australia and New Zealand had pets, who have been living longer and are considered part of the family.
"There's a whole range of things specialty pet does, it's very different to the dog and cat food we sell in the supermarkets," he said. "And so we're very, very keen to engage and to make those opportunities available to our customers."
The purchase price values the company at $1.7 billion, 11 times Petspiration's earnings before interest, tax, appreciation, depreciation and amortization (EBITDA) of $157 million for the year to September.
The PETstock franchise was founded by brothers David and Shane Young in 2002 in regional Victoria, based on the foundations of Ballarat Produce and Merchandise, which their family had acquired in 1991.
The brothers will continue to lead the business, Australia's second-largest pet product chain.
"We believe in the Youngs, they are two of Australia's great entrepreneurs," Mr Banducci said.
"It's a privilege to be investing alongside them, to help them realise their vision for this business, and to provide some of the Woolworths capabilities to help that vision be realised."
The $586m purchase will be funded from the $636m Woolworths made when it sold down its stake in pub and bottleshop chain Endeavour Group.
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