It expects to do that in the second half of 2015.
EBay's chief executive John Donahoe said: "A thorough strategic review... shows that keeping eBay and PayPal together beyond 2015 clearly becomes less advantageous to each business strategically and competitively."
PayPal's revenues are growing at 19% a year, twice as quickly as eBay's.
Its payment system is available in 203 markets worldwide and is expected to process 1 billion mobile payments this year.
PayPal's annual revenue is $7.2bn (£4.5bn), while eBay's is $9.9bn and is growing at 10% a year.
The move marks a reversal of strategy for the company.
Resistance
Mr Donahoe, said: "The industry landscape is changing, and each business faces different competitive opportunities and challenges."
Earlier this year the activist investor, Carl Icahn, began pressing for eBay to sell PayPal, a plan that was resisted by the eBay board. He stopped pushing after failing to gain enough support.
EBay's shares were 11% ahead of the official start of trading in New York.
EBay bought PayPal in 2002 for $1.5bn (£905m), and the payments company is now the Silicon Valley firm's fastest-growing business, with 143 million active users at the end of 2013, up 16% from a year earlier.
PayPal's new president and chief executive will be the current American Express co-executive Dan Schulman.
Meanwhile, Devin Wenig, currently president of eBay Marketplaces, will become the new chief executive of eBay.
Source: BBC News
