Hagger will see out her current contract, which ends in December this year, and continue to work on client business and key projects until then.
She was promoted to the role of chief integration officer in February this year, taking responsibility for establishing Glue's positioning within the Isobar network as well as shaping its new-business and marketing offering.
Her promotion was part of a management reshuffle that allowed Mark Cridge, Glue's chief executive, to give more time to his role as Isobar's global managing director.
Hagger was previously the managing director of the agency and, before that, joint managing director alongside James Sanderson.
Cridge said: "Jo has made a phenomenal contribution to the success of the business and will be sorely missed."