Marcus joined PayPal in 2011 and served as the vice president of its mobile payments business before he was named president in 2012.
"David reinvigorated product design to deliver compelling consumer experiences and energized the team to make a great business better," eBay CEO John Donahoe said in the announcement of Marcus' departure.
Facebook says its users send more than 12 billion messages every day and that more than 200 million people every month use Messenger, its standalone mobile app.
In its own press release, Facebook says it is "excited by the potential to continue developing great new messaging experiences that better serve the Facebook community and reach even more people, and David will be leading these efforts."
eBay said Marcus will remain with the company through the end of June, and while his successor has not yet been named, Donahoe said that Marcus "leaves behind a strong leadership team" and that the group is "committed to not skipping a beat on executing our plans, scaling product innovation, and driving global growth."