"They lived together and died together, so it was only right they went together too. I want them to go together holding hands."
The couple had been married for 60 years after tying the knot on March 27, 1954, and had daughters Sharon and Susan, nine grandchildren and three great-grandchildren.
Mr Bower was diagnosed with cancer in 2009 and had gone into remission, only for it to return last year.
Mrs Bower suffered from chronic obstructive pulmonary disease and had pneumonia when she died in the Northern General Hospital on February 17.
Sharon, 54, said: "They were really close and always together. Mum was in a wheelchair and on oxygen and because of that she never got to see him in hospital, which upset her.
"We were going to try and get her down, but he died the night before."
Sheffield funeral director Michael Fogg, based in Woodhouse, was happy to help the family with their unusual request.
Mr Fogg said it was the first time a double coffin had been used in South Yorkshire.