Darby will take on the role of chief executive on 4 February and follows Clarke's decision to stand down.
Clarke has agreed to "remain available" to the company until mid 2013 to ensure a successful handover to his successor.
Darby has a consumer goods pedigree. He spent 15 years at Coke in senior leadership roles, including a stint as marketing manager and marketing director. He then moved to Vodafone in 2001, where he was latterly chief executive of its non-European ventures.
His most recent role was as chief executive of Cable & Wireless, which he turned around before its eventual sale.
Clarke’s exit comes as the maker of Hovis works to cut its debt pile by selling off parts of the business.
These disposals have included Premier Food’s jam and jelly business, including Hartley’s, for £200m and its sweet pickles and table source business, which includes the Branston pickle brand, for £92.5m.
In November Premier Foods announced it was shutting two bakeries and axing 900 jobs.Follow @johnreynolds10