The former Scottish & Newcastle boss took on the role in November 2008 but said now was "the right time" to leave. He will be replaced by COO and FD Stephen Glancey.
"It has been a period of intense activity and with the strategic course of the business established, I have decided this is the right time for me to hand over the baton."
Chairman Sir Brian Stewart added that Dunsmore had "delivered a substantial turnaround and transformed the group during a period of economic turbulence".
On Glancey, he added: "Stephen has played a vital role over the past three years, including the successful acquisition and integration of the Tennent's and Gaymers businesses."
Kenny Neison will replace Glancey as FD.