Shares of Zynga, which also said founder Mark Pincus would be executive chairman, were up 8.8 percent in extended trading on Tuesday.
Gibeau, who joined Zynga's board in August 2015, has spent more than two decades at EA and most recently was executive vice president of EA's mobile games business.
Zynga, once one of Silicon Valley's fastest-growing companies, suffered a dramatic reversal of fortunes in 2012 as gamers switched from the company's Facebook-based desktop games to those played on mobile devices.
Other game makers are rapidly shifting to the highly addictive mobile gaming space to boost growth.
Activision Blizzard Inc, for example, said in November it would buy "Candy Crush" maker King Digital, giving it a bigger foothold in mobile games.
"We view Zynga as a business in desperate need of a radical turnaround," Cowen and Co analyst Doug Creutz said.
Creutz, however, said in a note that Gibeau was a console and PC veteran.
"We are not sure how much Gibeau's experience will benefit Zynga," he said. Pincus has been Zynga's CEO since Don Mattrick stepped down in April.
Mattrick's exit wasn't well received by the market at the time with some analysts saying the San Francisco-based company was beginning to move in the right direction under Mattrick.
Up to Tuesday's close of $2.16, the stock had lost more than a quarter of its value since Mattrick's exit.
Zynga last month forecast lower-than-expected bookings for the first quarter ending March as it expected to release only one game in the period.
© Thomson Reuters 2016
For the latest tech news and reviews, follow Gadgets 360 on X, Facebook, WhatsApp, Threads and Google News. For the latest videos on gadgets and tech, subscribe to our YouTube channel. If you want to know everything about top influencers, follow our in-house Who'sThat360 on Instagram and YouTube.