He will take over from Michael Wemms who has held the position for the past two years.
Mulcahy became group managing director at Kingfisher in 1984 and retired from the DIY group as chief executive in 2002.
He is chairman of retail consultancy group Javelin and a non-executive director for retailers Instore and The Home World.
BRC director general Kevin Hawkins said: 'Geoff will be a big asset as our next chairman. He is well known throughout the industry and brings a wealth of experience to the job. He also has experience of lobbying government. This is exactly the right mix of skills and knowledge we need for the role of BRC chairman.'
The appointment will take effect on July 1.
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