The twins were separated at birth and not told they had any siblings. They were adopted by different families, and - amazingly - as adults they met, fell in love and married.
The High Court ruled the marriage had never been valid and annulled it.
Further details of the case, and the identity of the twins, have been kept secret to protect them.
Professor Lord Alton, who uncovered the case, said: "The right for children to know the identity of their biological parents is a human right.
"There will be more cases like this if children are not given access to the truth."