Mr Saunders announced he would be leaving the organisation in May but will be remaining in an advisory capacity until the end of 2012.
Mr Godfrey spent 11 years as director-general at the Association of Investment Companies where he led a team through a series of regulatory challenges.
He has also been chairman of the Personal Finance Education Group (pfeg) from 1999-2003 and a member of HM Treasury's Financial Services Forum from 2006-2010.

Douglas Ferrans, IMA chairman, said: "After an exhaustive search process the Board is delighted to have recruited Daniel. Our objective was to find an individual capable of leading the IMA in the most challenging environment we have ever seen and we believe that Daniel has the integrity, experience and skills necessary to achieve that.
"The Board would also like to put on record our appreciation of Dick's achievements over the last decade at the helm of our Association and to offer him our good wishes for his future."
Mr Godfrey said: "I am looking forward to working with the talented team at the IMA, the Board, our members and the wider community of stakeholders, especially consumers and their representatives, to help the Association add value for investors."
He said a key task for him in his new role would be to rebuild trust in financial services.
"The IMA and the industry must identify and do whatever is necessary to earn trust by demonstrating the fundamental qualities of transparency and customer focus on which investment management is based.
"Secondly, we need to steer a path through the regulatory agenda so that consumers are properly protected without unnecessary costs or distractions that can only cause detriment by damaging long-term returns. The investment management sector can lead the efforts to restore trust."