Cox, who is close to Zuckerberg, started working for Facebook in 2005 as a software engineer at the company and contributed to launching several key applications such as News Feed.
Cox also held a number of senior positions in the company; he served as head of the human resources department and also in launching the Facebook Workplace platform.
Daniels began as a platform leader five years after managing the Internet.org initiative, which is helping to strengthen online communication around the world.
Will Cathcart, who currently heads the mobile phone application for Facebook, will succeed Daniels.
Cox did not announce his successor.
The changes came shortly after Zuckerberg announced his plan to turn Facebook into a "privacy-focused platform."
The social networking giant, with its two platforms, Whatsapp and Instagram, faced the worst malfunction in its history. Facebook blamed the crash for a server change.
The company said it had "launched a series of successive versions" of its platforms, including Whatsapp and Instagram.
The failure, which lasted more than 14 hours, prevented the use of the company's products around the world. Facebook did not explain during the entire day of the emergence of the problem any clarification, and said that everything has returned to normal, and added: "We are very sorry for the holidays and appreciate the patience of everyone."