The happy couple celebrated their vows with a party for close friends and family at a country mansion in the heart of the New Forest.
Dahl, the granddaughter of children's author Roald Dahl, met her husband-to-be at a charity event in London over two years ago and were engaged last spring. The couple live together in west London.
Cullum, 30 recently told the Daily Mail's Live magazine that falling in love with Dahl, 32, changed him for the better: "'My relationship with Sophie has helped put everything in perspective," he said, adding: 'It reminds me that while I love (working), and have certain responsibilities to my career, there are more important things in life."
Cullum is due to release his fifth record, The Pursuit, in the U.S. in March, and will tour stateside to support it.