Linder replaces the outgoing David Wheldon, who joins Vodafone later this year in a senior role reporting to the global brand director, David Haines.
However, Linder will retain an overarching role on the BP business, on which O&M's London office is the lead agency. John Seifert, the global account leader based in the US, will continue to run the account.
A replacement for Linder has yet to be announced, but an internal appointment is expected within weeks.
Linder will be charged with broadening WPP's tenure of the Vodafone business.
Until now, the holding company, through JWT, has acted as Vodafone's global network, with Wieden & Kennedy as the creative supplier, providing an overall strategy.
Linder's CV, which extends across both the creative agency and client arenas, includes long stints at Ogilvy Worldwide, where he was the executive group director, and Young & Rubicam
Most recently, he headed Ogilvy's Detroit office and served as the worldwide client service director on Ford, McKinsey & Company and Arthur Andersen, before relocating to London in 2001.
Linder first made a name for himself at KPMG, where he was responsible for positioning the accounting and consulting company as "The global leader".