Former BBC news correspondent Peacock has been at Vodafone for more than six years, "establishing one of the world’s leading corporate transparency programmes" during his time at the telecoms giant.
He will leave to pursue a portfolio career including writing books, university and business school lecturing and advisory/non-executive roles.
Joining in 2011 from global oil and gas exploration and production company BG Group, Peacock also had stints as comms director with Ofcom, mobile network operator Three and AOL.
Vodafone Group chief executive Vittorio Colao said: "Matt has developed and implemented a very successful communications strategy for Vodafone, providing the Group with wise advice and expert support through all of our major corporate developments and transactions over the last seven years. He has been extraordinarily rigorous and passionate in working to enhance Vodafone's reputation, providing very sensible and highly informed advice on an enormous range of issues.
"Matt has also reshaped the Group’s approach to sustainability, including establishing one of the world’s leading corporate transparency programmes. I would like to thank him for the significant contribution he has made to Vodafone."