Montagu is currently chairman of the Aviva UK Life With-Profits Committee and a director of the Pension Corporation and is a former chairman of the Board of Inland Revenue.
He will replace the current chairman of the FOS, Sir Christopher Kelly who is stepping down in January after seven years in the position and an additional three years as a non-executive director.
Natalie Ceeney will remain the chief executive and chief ombudsman of the service and in charge of investigating individual disputes, while Montagu will take over the role of leading the board of nine non-executive directors, determining strategy and ensuring Ceeney delivers that strategy.
In an interview recently for the FOS, Kelly said his most challenging task as chairman had been "responding to the challenges posed by payment protection insurance" both operationally and legally.
He added that in an increasingly technology-driven world the FOS might have to adjust its time-scales as it "might no longer be realistic to expect people to wait eight weeks before the ombudsman service can step in".
The FOS is funded in practice by a tax on the financial services industry and the FSA is in charge of appointing its chairman and approving its annual budget.
Every three years the board commissions an independent external review, with the last one published in 2008 and one currently being carried out by the National Audit Office.