The PFRA announced today that de la Bedoyere, who has been in post since August 2012, will leave at the end of October.
De la Bedoyere, who joined the PFRA from the RSPCA, will take up her new role in November.
Blue Cross has been without a chief executive since January, when Kim Hamilton stood down amid allegations made in the national press about her love life.
The PFRA said in a statement that de la Bedoyere had led it through Lord Hodgson’s review of the Charities Act 2006 and subsequent inquiry by the Public Administration Select Committee.
It said she had also overseen the development of an automated allocation system for street fundraising and had worked with the Institute of Fundraising and the Fundraising Standards Board to commission the professional services firm PwC for a report on the future of fundraising self-regulation.
The report concluded that the PFRA, the IoF and the FRSB did not trust each other enough to be able to work in partnership to deliver self-regulation effectively, Third Sector revealed in July.
Paul Stallard, chair of the PFRA, said: "Sally has helped to transform the PFRA in just two years and I have every confidence she leaves behind a strong team and legacy from which we can continue to strengthen both the PFRA and face-to-face fundraising.
"We will now seek to appoint a successor to continue the established direction of travel and further develop our close working alliances with both the IoF and the FRSB."
De la Bedoyere said she would look back on her time at the PFRA with great affection. "I have hugely enjoyed my time at the PFRA, working directly with some great charities and their suppliers," she said. "I shall miss the team but know they are well placed to continue the important work of the PFRA."