The unnamed man became a donor after his son and daughter-in-law could not conceive a child through IVF (in-vitro fertilisation) because his son's sperm was not of high quality, London's Evening Standard newspaper reported.
His son will become the father of his genetic half-brother, the paper pointed out.
The sperm is being screened at the London Women's Clinic, which is treating the couple who are in their 30s and who have requested anonymity.
The clinic's co-medical director, Doctor Peter Bowen-Simkins, told the daily he had never seen such a case before, but some people are now willing to consider all kinds of options with progress in fertility treatment.
"Obviously the wife's mother-in-law also had to be included in all the conversations but she has no objections," he was quoted as saying.
"Society has also changed its perceptions of what is and what is not acceptable. In this case, keeping the identity of the child similar to their own was a huge factor.
"The husband does not have a brother, which is why he chose his own father to assist."
A spokeswoman for the Human Fertilisation and Embryology Authority (HFEA), which regulates the fertility sector in Britain, said it did not need to approve the decision.
Donations from family members, including sisters sharing their eggs, are permitted under British law, she said.