Activist hedge fund Elliott Management announced a $1.4 billion stake in eBay in a letter to the e-commerce company's board on Tuesday. Fellow activist investor Starboard Value has also built a stake in the company, people familiar with the situation told CNBC's Thomas Franck.

Elliott's stake, which represents more than 4 percent of eBay's shares, comes with an extensive letter of recommendations for the company's future. The fund's "Enhance eBay Plan" suggests the company spin off StubHub as well was eBay's "portfolio of Classifieds properties," as Elliott said the assets "are worth meaningfully more than the value currently being ascribed to them as part of eBay."

Fellow activist investor Starboard Value also has a notable eBay position, sources told CNBC. The Wall Street Journal reported that the stake is less than 4 percent and was taken more than six months ago. A person familiar with the matter told the Journal that Starboard has talked to eBay about similar changes to those Elliott recommended. Starboard did not respond to a CNBC request for comment.

Shares of eBay closed trading up 6.1 percent at $32.90 a share, after being up as much as 10 percent earlier in the day.

@davidfaber: Elliott takes new $1.4b position in $EBAY. Wants company to separate Stub Hub and classifieds business. More on @SquawkStreet

Elliott also said eBay should focus on "revitalizing Marketplace," clean up "an inefficient organizational structure" and stabilize the company's leadership, which "has suffered an alarming degree of turnover recently."

The fund estimates that its "Enhancing eBay Plan" would nearly double eBay's value to $55 a share by the end of next year, even without spinning off the StubHub and Classifieds businesses.

Elliot Management has about $34 billion in assets under management, according to the fund's website.