Baughan has been chief executive of Maxus since 2014, when he was promoted from managing director. He joined Maxus in 2012 from fellow WPP agency Mindshare, where he was head of business development.
Chief executive of Maxus North America since June 2014, Williams was previously UK chief executive at OMD Group until 2012 when he moved to PHD New York as president.
Maxus’ chief strategy officer Damian Blackden will take the same role at Essence.
Williams, Baughan and Blackden will report to Christian Juhl, global chief executive of Essence.
Juhl said: "We have felt incredibly well-supported by Group M since joining their ranks a year and a half ago. And, this new infusion of truly top-tier talent into Essence is yet another example of WPP’s ongoing commitment to our success."
Essence has also appointed Group M’s head of data and analytics strategic development Simeon Duckworth to the role of global head of strategy and analytics and Garrick Schmitt, co-founder of the digital product and service company Junior, as global director, experience design.