PetSmart has made the biggest e-commerce acquisition in history, snatching up fast-growing pet food and product site Chewy.com for $3.35 billion, according to multiple sources familiar with the deal.

The deal is a huge one by any standard — bigger than Walmart's $3.3 billion deal for Jet.com last year — and especially for a retail company like PetSmart that was itself valued at only $8.7 billion when private-equity investors took it over in 2015.

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But Chewy.com has been one of the fastest-growing e-commerce sites on the planet, registering nearly $900 million in revenue last year in what was only its fifth year in operation. The company had been a potential IPO candidate for this year or next, but was taken out by its brick-and-mortar competitor before that.

Chewy was founded in 2011 by Ryan Cohen and Michael Day and built a cult following for its excellent customer service, large selection and fast shipping. It had quietly raised at least $236 million in venture capital from investors including Volition Capital, T. Rowe Price and BlackRock.

Its under-the-radar status was probably aided by the fact that it was headquartered in Fort Lauderdale, Fla. and not a big e-commerce market like New York, Los Angeles or Seattle. But it did have a big name in the industry as chairman: Mark Vadon, who also co-founded Blue Nile and Zulily.

The deal is the type of bet-the-company acquisition by a traditional retailer that commerce-focused venture capitalists have been betting on for some time.

PetSmart had announced its intention to acquire Chewy on Tuesday morning, but didn't disclose a price. PetSmart is owned by a group of private-equity investors led by BC Partners.

—By JASON DEL RAY, Recode.net.

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Watch: PetSmart goes private