Pennycook, who will take up the role on an interim basis, joins after nearly eight years as group finance director at Morrisons.
Before this, he held the same role at both RAC and JD Wetherspoon.
Pennycook said he was “delighted” with his new role.
“I am delighted to be joining The Co-operative Group to help drive its development. With its strong brand and loyal customer base, the Group is ideally positioned to address the challenges it now faces.”
Meanwhile, Richard Pym was appointed chair of The Co-operative Banking Group and The Co-operative Bank.
Euan Sutherland, group chief executive of The Co-operative Group, said: “Both have fantastic track records in British business and the team and I look forward to working closely with both of them.
“Richard Pennycook has proven long-term experience working at the top of some of Britain’s leading companies and will make a valuable addition to our organisation.”