Blackwell, who will join the CRA on 5 January, replaces Warren Alexander, who retires at the end of January.
Blackwell has been at the ATCM for 10 years, the past four as chief executive. He spent six years as chief executive of Towns Alive – formerly Action for Market Towns – which promotes small towns.
He worked for 20 years at the retailer WH Smith: he joined as a teenager and worked his way up to manage stores. He also owned an independent book shop.
Ben Merrett, chair of the Charity Retail Association, said Blackwell would bring a "wealth of retail and membership experience".
Merrett said: "He brings a proven track record in business, the voluntary sector and strategic policy engagement at the highest levels."
Blackwell said charity shops did "an untold amount of good work for charities, high streets and people".
A CRA spokesman declined to reveal what Blackwell’s salary would be.