His appointment follows the departure of Gary Leih, who resigned from his position as chairman and chief executive of Ogilvy Group UK in July.
He will head the agency and report to Paul O’Donnell who replaced Leih in the group role.
Baillie has previously worked at Grey London and Saatchi & Saatchi before joining BBH in 1998.
Ogilvy Advertising has also appointed BBH planning head Rachel Hatton as planning director.
In addition, Hatton will lead planning across the Ogilvy Group UK.
She replaces John Shaw, who has taken on the position of joint global planning director.
Hatton previously worked at BMP and on the Labour Party’s election campaign in 1997. She joined BBH in 2000 and has most recently led planning on the Audi and Britvic accounts.
Both are expected to start in the new year.