Founded in 2010 by former ITV and Camelot executive Gallagher, the agency now has around 30 full-time staff, and clients include Airbnb, Centrica, John Lewis, drinks firm AB InBev and tobacco giant Philip Morris International.
Foster, who also worked at ITV, helped set up the agency and had held the role of managing partner for the past year. He became the agency's first CEO on 1 January, with clients and staff having been informed of the change at the end of 2016.
While Pagefield will remain Gallagher's foremost priority, he is understood to be keen to spend more time on charity, political and Brexit-related work. He is an adviser to the Archbishop of Canterbury as well as to various charities, and was also one of few prominent PR agency bosses to publicly back an exit from the European Union.
Foster said: "As PRWeek itself has predicted, we’re an agency to watch in 2017, and I’m confident that the dedicated and brilliant group of people across the Pagefield team will prove that prediction to be accurate by the end of the year."
Gallagher said: "Oli has been doing a fantastic job as our managing partner for the past year or so and this appointment confirms my confidence in him."