His decision was announced yesterday by the charity, which has not been afraid to court controversy under Grant’s leadership and earlier stint as director of communications and campaigns between 1988 and 1991.
Grant stepped down with immediate effect "because of medical concerns about his health", according to the charity, which added that deputy chief executive John Grounds would cover Grant’s public commitments as appropriate and continue to represent the charity externally while it searched for Grant’s successor.
Grant has held a number of roles over his career but is particularly associated with WPP agency Burson-Marsteller, which he joined as chairman of public affairs in 1999.
He was with the agency for 12 years and was its chairman when he resigned in 2011 to take the RSPCA job.
He has also worked as director of global corporate and public affairs at The Body Shop and director of public affairs at the Association of Unit Trusts and Investment Funds.
Grant said of his resignation: "It has been a huge honour to have held this post. The RSPCA is a magnificent organisation at the heart of what is the very best in humanity. The society is blessed with great people both paid and volunteer. I wish it well as it continues to face huge challenges in ensuring it is ever stronger and able to meet the needs of our fellow creatures."