The couple tied the knot before close family members, at their palatial new Perthshire home, Rowling's agent confirmed.
The 35-year-old millionaire author and Dr Murray, 30, bought the secluded 19th Century mansion in the autumn.
Rowling's tales of the boy wizard's exploits have become a publishing phenomenon, with thousands of adults, as well as children, becoming firm fans of the series.
Intimate gathering
According to the News of the World, Rowling wore a cream outfit, especially designed for her, at the ceremony and her eight-year-old daughter, Jessica, was one of three bridesmaids.
The others were said to be Ms Rowling's sister Dianne, 33, and Dr Murray's sister Lorna.
It is thought that only about 15 guests attended the wedding which the couple had reportedly been anxious to keep secret.
Rowling guards her privacy fiercely and in October won a complaint against OK! magazine which published pictures of her family holiday.
She has been married once before - to Jessica's father, Portuguese journalist, Jorge Arantes - but the relationship was shortlived.
Sales soar
Earlier this month, sales figures revealed the first Harry Potter novel - released four years ago - is the UK's biggest-selling book of 2001.
Sales of Harry Potter and the Philosopher's Stone have been boosted to 1.1 million by the release of the film adaptation, which has broken box-office records across the world.
The film of the second book, Harry Potter and the Chamber of Secrets, is already in production and scheduled for release in the middle of next year.
Four books have been published so far but Rowling has always said there would be seven in the series - covering one Hogwarts school year at a time.
The final chapter of the last book has already been written, she told the BBC last week.
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