The Pogues frontman and his long-term partner tied the knot in a ceremony attended by their closest family and friends, including Hollywood actor Johnny Depp.
The couple, who go back 32 years, said 'I do' in a private celebration in Copenhagen City Hall after revealing just days ago they were to be wed after an 11-year engagement.
The beaming bride wore a long-sleeved, V-neck red dress by Bella Freud London, after previously revealing she would be foregoing the traditional white dress. She also wore a fresh flower crown and carried a hand-tied bouquet of red roses and green foliage.
Groom Shane donned a black suit jacket, navy trousers and black tie, topped off with a black trilby hat.
Despite not going down the traditional wedding route, the couple did include the bride's mother and sisters on flower and wedding cake duty, and her nieces did her make-up.
Clarke previously revealed the couple wanted to elope and keep it secret, but also knew people wanted to share in their happy day.