The deal is Amazon's largest acquisition to date. Zappos' investors, who were reportedly eager to cash-in, despite the company's inspiring performance through the recession, will receive 10m Amazon shares, worth $888m.
An additional $40m in cash will be paid out to Zappos employees.
Zappos was launched in 1999 by Hsieh, who modelled the company after Amazon. It is backed by venture capital fund Sequoia, best known for its early investments with internet giants Google, YouTube, PayPal and Yahoo!.
The company will continue to operate as a separate brand to Amazon, which also runs its own online shoe business, Endless, launched in 2007 and allegedly copied from Zappos' own business model.
Zappos grossed nearly $1bn in merchandise sales last year and is known for its cult like following among customers, and in turn, for its attentive approach to customer service.
The company offers free shipping for its products, with an open returns policy, and is a leader among retailers for embracing social networking -- the company has more than one million followers on Twitter.
Bezos, on YouTube (video announcement below), said: "I get weak-kneed when I see a customer obsessed company, and Zappos certainly is that."
In a letter to employees, also posted on Twitter, Hsieh wrote: "We've been on friendly terms with Amazon for many years, as they have always been interested in Zappos and have always had a great respect for our brand.
"Several months ago, they reached out to us and said they wanted to join forces with us so that we could accelerate the growth of our business, our brand, and our culture.
"When they said they wanted us to continue to build the Zappos brand (as opposed to folding us into Amazon), we decided it was worth exploring what a partnership would look like."
The deal is set to close by fall. Amazon said Zappos management set-up will remain as it is. Zappos is the latest in a number of acquisitions for Amazon, which has purchased other online firms, such as IMDb and Alexa.