EBay would gain expertise in helping major retailers fill online orders and build relationships with big toy, electronics and book sellers which have helped Amazon grow.
EBay said on Monday it had offered GSI shareholders $29.25 per share in cash, a premium of 50.9 percent from the stock's closing price on Friday.
The deal would be eBay's largest acquisition since it bought Internet phone company Skype for $2.6 billion in 2005, and comes as growth in its main auctions business is slowing.
"It's one of the few fulfillment operations that could rival Amazon," BGC Partners analyst Colin Gillis said. "Amazon is fulfilling its third-party sellers more and more. eBay is all third-party sellers."
On Nasdaq, GSI soared 50.7 percent to close at $29.20, while eBay fell 4.3 percent to $30.34 on concerns it may be paying too much and might eventually need to invest more money on GSI's technology. Both stocks held steady in extended trading.
Amazon shares edged down 1 percent to end at $169.35.
Among GSI's clients are Aeropostale Inc, Toys R Us, and TJX Cos Inc's Marshalls chain.
GSI, which owns Web businesses such as Rue La La and ShopRunner, also provides retailers with technology, payment processing and customer care services for their e-commerce operations.
Online shopping accounts for about 8 percent of total U.S. retail spending, rising 11 percent during the most recent holiday season, according to data firm comScore, almost twice the pace of bricks-and-mortar sales.
EBay estimated in February that its online marketplaces unit is set to grow into a $7-8 billion business by 2013, from $5.7 billion in 2010. In contrast, Amazon pulls in annual sales of more than $30 billion.
While PayPal has been a growth driver for eBay, the company has struggled with other deals, such as its purchase of 28.4 percent of classifieds site Craigslist, which led to a court fight after eBay launched its own classifieds business.
Still, Fred Moran, an analyst with Benchmark Capital, called the price "reasonable," saying it comes out to 13 times this year's expected earnings before certain expenses, which he said "is right in line with the e-commerce peer group."
UNLOADING MOST OF RUE LA LA
As part of the deal, eBay would sell off GSI's licensed sports merchandise business, as well as 70 percent of Rue La La, which offers one-day-only Web deals to its members, and ShopRunner, a members-only online shopping service that offers free shipping.
EBay said those business were not important to its long-term growth strategy.
Those holdings would become part of a new company run by GSI founder and Chief Executive Michael Rubin. EBay said it would lend Rubin's new company $467 million, bringing the deal's value to $2.4 billion.
EBay said the acquisition, expected to close in the third quarter, would have little effect on its fiscal 2011 adjusted earnings forecast, and boost 2012 earnings. The deal would hurt 2011 net income by 30 cents to 34 cents per share, the company said.
GSI has until May 6 to solicit bids from other parties during the so-called "go shop" period.
While PayPal has been driving eBay's growth for years, the company is also trying to lift its more familiar marketplaces unit -- a high-margin but mature business that connects online buyers and sellers -- especially as Amazon has enjoyed double-digit revenue growth.
The GSI deal follows a number of other e-commerce deals in recent months. Amazon expects to close its purchase of Quidsi, operator of diapers.com, around April 1. In November, Oracle Corp said it would buy e-commerce software company Art Technology Group Inc for $1 billion.
Goldman Sachs & Co, and Peter J. Solomon Company are acting as financial advisers to eBay, while Dewey & LeBoeuf LLP is its legal adviser. Morgan Stanley is advising GSI and Davis Polk & Wardwell LLP is advising a special committee of GSI's board. Morgan, Lewis & Bockius LLP is acting as GSI's legal advisor.