The agency already held the Staples account, worth £4.7m, while John Ayling was the incumbent on the Office World account.
The account came up for review when Staples bought Office World last year and decided to consolidate its media account.
It is understood that ZenithOptimedia beat John Ayling and two other agencies, including MediaCom, for the brief.
A John Ayling spokesman confirmed they had lost the pitch.