Stephenson will take on the newly created role of senior director of category development at the digital media platform.
It is not known if he will be replaced at the COI, which has cut staff by 40% following the freeze in non-essential marketing spending. Its future shape and role is also currently under review by the Cabinet Office.
The Government’s marketing services provider recently lost director of channel integration Corrine Purton and deputy chief executive Peter Buchanan, who retired last month.
Stephenson spent nine years at the COI and is said to have overseen digital campaigns including Armed Forces Recruitment, swine flu, FRANK and knife crime.
In July, the COI said it would increasingly turn to digital media to help deliver public information campaigns for less money.
The Cabinet Office, however, wants to utilise Government websites to deliver messages.