Nunn, also a former director of the Charities Aid Foundation, will take over the role of director in March.
Nunn left the Social Investment Business - formerly Futurebuilders England - which administers government-backed loan funds worth £400m, in April this year after nine months in the post. Before that, she spent three years at CAF, where she was director of business development.
"We were keen to appoint someone with experience of the sector and a keen understanding of the issues that we face," said David Prescott, chair of the fund. "We are delighted that Gill brings this, along with great enthusiasm for what we are looking to achieve."
The CEBF, which was set up to help charity workers in financial difficulty, was officially launched in November.