Dame Barbara will tell the story of Americans Abbott and Costello who she watched during her teens.
She said: “I absolutely loved them. I’m happy to pay tribute to them as two of America’s leading funnymen.”
Radio 2 boss Lewis Carnie added: “I was delighted when Barbara agreed to narrate this documentary profiling one of the world’s most talented double acts.”
Former EastEnders and Carry On actress Barbara and her husband, Scott Mitchell, 55, revealed earlier this year that she was diagnosed with the onset of Alzheimer’s in 2014.
Her radio episode was recorded in April, shortly before she went public.
During the series actor Christopher Biggins will tell the story of British female comedy act Gert and Daisy.
Singer and actor Michael Crawford’s episode will be about Laurel and Hardy.
● Double Acts, BBC Radio 2, July 25 at 9pm.