Amjid Ali, from Bristol, began a campaign for the changes in 2013 and has been working for the NHS.
Muslims are allowed to accept transplants, but previously some had not felt able to donate themselves.
Ali said: "It was something I wanted to give back, having been on dialysis and the waiting list for a long time."
NHS figures show that 17 per cent of people on the transplant waiting list are of Asian origin. However, less than 2 per cent of Asian people are on the organ donor register.
In September 2013, Ali led a conference with 56 scholars, organisations, imams and chaplains about the issue, two years after his own life-saving operation.
"Many Muslims feel [organ donation] is not in line with their faith," said Ali, who is the NHS lead on the Transplantation in Islam project.
"They needed an authoritative religious figure to be able to give them the satisfaction that they've researched the subject in such a way that covers all of the key points around the permissibility of organ donation."
He also posted a tweet after his success.
Two fatwas were issued in 1995 and 2000 but were aimed at Arab Muslims. Now another, for the Sunni community, has also been issued. This new fatwa complements the previous fatwas and is aimed at British Muslims who are predominantly of south Asian background and heritage.
Scholar Mufti Mohammed Zubair Butt, who issued the fatwa, said he hoped the move would help to "serve as a catalyst" for change.
The edict covers all forms of donation, including blood, stem cells, living donation and organ donation after death.
It is a refreshing development given the fact that the situation isn’t the same everywhere, as some religious leaders are not in favour organ donation. For example, a madrasa in Kanpur in the Indian state of Uttar Pradesh issued a fatwa against a Muslim man, Arshad Mansuri, after he pledged to donate his organs to people in dire need.
The fatwa, issued by a cleric Maulana Hanif Barkati in March last year, also asked the Muslim community to boycott him.
"Mansuri had asked me how organ donation is considered in Islam. I replied that it's banned. Someone who doesn't follow what Allah has said, then there're doubts on him being a Muslim," Barkati had said.
"Mansuri could be a man who has just kept a Muslim name and is trying to defame Muslims," he asserted.