Mapp, who starts his new role on 1 December, is the successor to Lord Myners, who left the position in October after six months.
Mapp is currently non-executive chairman of the FTSE 250 media company Informa, non-executive chairman of Salmon Developments and executive chairman of Imagesound. He was formerly chairman of the British Amateur Boxing Association.
Andy Boland, a non-executive director of Huntsworth, said: "We have completed our search and we are delighted that such a strong candidate as Derek has agreed to lead the Huntsworth board as chairman and we look forward to working with him."
Mapp said: "I am excited to be joining the board of Huntsworth as its chairman and look forward to working with the board to take the business forward in its next stage of development."
Huntsworth, the parent company of Grayling and Red, is still looking for a chief executive to replace Lord Chaddlington, who is due to retire when his successor is found.