He will arrive at the agency on 26 June, working under political division chair Tim Collins.
Chapman was most recently chief of staff to Brexit secretary David Davis, working in the new Department for Exiting the European Union.
Prior to this role, Chapman was director of comms for then Chancellor George Osborne at the Treasury - during which time he was seen as positioning Osborne as a candidate for future Prime Minister.
Before entering government comms he was a journalist, latterly spending six years as political editor of The Daily Mail.
Collins said: "This is a very significant hire for us, and our clients will benefit hugely from the breadth of James’ experience at the Treasury, Department for Exiting the European Union, and on Fleet Street."
The agency said the appointment had been approved by independent public body the Advisory Committee on Business Appointments.
Bell Pottinger had "a year of consolidation and change" in 2016, according to boss James Henderson, with famous co-founder Lord Bell leaving the business. While PRWeek estimates for the Global Agency Business Report suggest revenue was down, Henderson said the firm performed "credibly" in difficult circumstances.