Robertson has chaired the UK division at global ad agency since 2006, and will remain in the role while fulfilling board duties at -- the joint venture company set up in 2007 by and business consultant Carole Stone.
Robertson will help YouGovStone expand its international influence and will be involved with TheStoneClub, launched to bring together industry minds to discuss and exchange ideas.
Nadhim Zahawi, chief executive officer of YouGov, said: "Kate Robertson shares our belief in YouGovStone's potential for growth.
"At a time when the views of opinion formers from across the world are increasingly important to management teams everywhere, Kate's insights and extensive international network will further strengthen the company."
Robertson said: "YouGovStone's polling and research have proved to be scarily accurate and extremely useful to many UK companies in recent months and personally I'm honoured and fascinated by their work and look forward to developing their reach."