Williams will be based in New York when he joins on 1 June, and will report jointly to Vikram Sakhuja, the global chief executive of Maxus, and to Kelly Clark, the chief executive of WPP’s media-buying arm Group M in North America.
He will lead its offices in Chicago, Los Angeles, Minneapolis, New York and Toronto.
Prior to taking the role of president on PHD New York for two years, Williams was chief executive of PHD’s sister agency OMD Group in the UK from 2007 to 2012, overseeing 550 people. He was not replaced when he left.
OMD Group is owned by Omnicom and includes OMD UK, Manning Gottlieb OMD and M2M in the UK.
Sakhuja said: "Steve has a great reputation as a leader and a client partner. He has a terrific track record of success in both the UK and the US, and he is a perfect fit for the ambitious Maxus culture."
Williams said: "I am excited to be joining Maxus and Group M. I am thankful for the incredible journey with Omnicom Media Group, but I’m now looking forward to a new journey with Maxus, who are uniquely positioned to grow locally and globally. I love the team’s energy and ambition."
Maxus has been the fastest-growing media agency in the world for the past four years, according to Recma.
Clark added: "We are confident that Steve will help us take Maxus to a new level. I know from competing against Steve that he can be a very potent force, so I’m delighted he’s now on our team."
Jones is retiring after five years in the role.