Cox worked on some of Facebook's key products, including the social network's News Feed, and led the product and design teams.
Media reports cite sources inside Facebook who said the new privacy focus was partially why Cox chose to leave.
Zuckerberg said Cox first mentioned he might leave a few years ago, but chose to stay on after 2016 as evidence emerged that Russians had manipulated Facebook's services to provoke discord in the USA and influence the election won by President Donald Trump.
"We have a clear plan for our apps, centered around making private messaging, stories and groups the foundation of the experience, including enabling encryption and interoperability across our services", Zuckerberg stated in his goodbye note to Cox.
Cox was in charge of Facebook's apps including its flagship social media site, as well as Instagram, WhatsApp and Messenger.
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Cox, who dropped out of a Stanford University graduate degree program to work with Zuckerberg when the company had just 15 engineers, was widely seen as one of the most popular and capable executives at the social network - and a potential replacement CEO, were Zuckerberg to leave.
The departures come less than two weeks after Zuckerberg announced a shift in Facebook's focus toward privacy after years of criticisms over the company's handling of users' personal data. He also built Facebook's first human resources teams and oversaw the strategy for the apps that Facebook owns, Zuckerberg wrote.
Facebook isn't hiring another executive to replace Cox. "This will be a big project and we will need leaders who are excited to see the new direction through", he said in a statement.
Daniels has been at Facebook almost nine years, and previously led the company's Internet.org effort, a project aimed at bringing internet access to developing countries. The longtime Facebook executive Will Cathcart will head up WhatsApp.
The departures follow the resignations of Instagram founders Kevin Systrom and Mike Krieger and WhatsApp's co-founder Jan Koum past year.
Numerous changes Zuckerberg outlined involve duplicating some of WhatsApp's features in Facebook's other messaging apps.