Neither Cox nor Zuckerberg specified what led to their split. Zuckerberg wrote that Cox considered leaving years ago to pursue new projects, but he made a decision to stay in 2016, around the time Facebook began taking heat for acting as a conduit for misinformation and Russian election interference.
The move comes with Facebook struggling to cope with investigations and complaints over data protection and privacy, and after Zuckerberg's announcement last week of a new focus for the platform.
Cox is among Facebook's highest-ranking executives and has been at the company for more than 13 years.
And just more than a week later, two of its biggest executives are leaving the company.
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Mr Zuckerberg, 34, Facebook chief executive, said last week that the company would shift away from publicly shared content on its site and focus on encrypted, private conversations across the messaging services WhatsApp, Instagram and Messenger. Daniels is leaving less than a year after WhatsApp founder Jan Koum resigned in an apparent dispute with Zuckerberg over the future direction of the widely used messaging service. "But after 2016, we both realized we had too much important work to do to improve our products for society, and he stayed to help us work through these issues and help us chart a course for our family of apps going forward", Zuckerberg wrote.
The departures of Cox and Daniels come a day after a technical issue that limited use of Facebook and Instagram for most of Wednesday. "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. Meanwhile, Javier Olivan will lead the effort to better integrate the Facebook apps.
These two departures come on the heels of founding-executive departures at Facebook-owned Instagram and WhatsApp previous year.
Facebook's social network and Instagram photo app won't change, and will remain available for sharing places, adventures and minutiae with a broader audience.