Templeman, whose retirement from the department store chain was announced in April, will join the trade body for the UK retail industry on 2 October.
He takes over from incumbent Luke Mayhew, who steps down on 1 October.
Stephen Robertson, BRC's director general, said: "Rob is a heavyweight in the world of retail.
"His huge experience and formidable knowledge of the big issues that the sector faces, make him an ideal chairman for the BRC as we work to help create a vibrant and sustainable retail industry for the future."
Templeman has held numerous posts across the UK's retail sector. Before joining Debenhams eight years ago, he was chairman of Halfords, chief executive of Homebase, and chief executive of Harveys Furnishings.
Templeman said: "I am really pleased to be asked to chair the BRC and look forward to working alongside Stephen and the team.
"Retail is one of the UK’s largest employers. It represents an important part of the country's economy and the BRC has proven to be the authoritative voice for the industry."
Debenhams is replacing Templeman with deputy chief executive Michael Sharp.