Sir Montague was appointed chairman of Aviva in April 2015, having joined as a non-executive director in January 2013.
He has previously held roles at law firms, Linklaters and Paines. In 2008, he held the role of chairman of British Energy from 2002 for seven years.
He originally joined the insurer as a non-executive director two years earlier.
He said: “When I became chairman in 2015 the board asked me to commit to serve for at least five years. Now that Maurice has launched Aviva’s strategy, a new senior management team is in place and the board has been refreshed, it is also time for a new chairman.
“In the meantime I remain committed to this great organisation which I am confident will deliver for all its customers, employees and shareholders.”
George Culmer, senior independent director, added: “Adrian has chaired Aviva through a period of considerable change and departs with our very best wishes for the strong legacy he leaves.”