The international chaplain takes up the post of CMS executive leader after five years as chaplain of St Michael's, a large multicultural church in the centre of Paris.
The church community at St Michael's includes French, English and Tamil speaking congregations and more than 40 nationalities.
He has developed the church's international connections in Africa and Asia and acted as consultant and companion to a Turkish-language church in Istanbul.
His past experience also includes a variety of positions at CPAS, including Acting General Director, and leading a multicultural church in Streatham, south London.
Rev Mounstephen said he was "thrilled and delighted" to lead the CMS community in mission.
"I look forward to working in life-changing mission with partners the world over who share our abiding passion – that the world would know Jesus Christ,” he said.
John Ripley, the Chair of CMS trustees, said Philip was "a very strong communicator and influencer".
"We are very grateful to God and are confident that Philip will inspire the whole CMS community and engage all sorts of new audiences," he said.
Rev Mounstephen succeeds the Rt Rev Tim Dakin, who is now Bishop of Winchester.
He is due to take up his post at CMS in October, when he will meet colleagues from the
collaborative international network made up of CMS, CMS Africa, AsiaCMS and New Zealand CMS.