EBay is hoping the transaction will bolster its ability to connect buyers and sellers around the world. It could also help the San Jose, Calif. become more of a competitive threat to Amazon.com Inc.
As part of the acquisition, eBay plans to sell GSI's licensed sports merchandise business and 70 percent of shopping sites RueLaLa.com and ShopRunner.com.
The $2.4 billion total would be the second-largest amount eBay has paid for another company thus far - in 2005 eBay paid at least $2.6 billion for Internet calling and messaging service Skype, which it has since sold.
A special shareholders' meeting to vote on eBay's offer will be held on June 17 in King of Prussia. GSI shareholders of record on May 9 will be allowed to vote at the meeting.
The acquisition is expected to close as early as the end of the second quarter.
GSI runs websites, packs and ships products, and offers interactive marketing services to a variety of retailers. It has long-term contracts with various retailers, including Radio Shack, Ace Hardware and American Eagle Outfitters Inc.
GSI's stock dropped 9 cents to $29.06 in afternoon trading.