The intimate ceremony was conducted by British Consul General Nick McInnes and attended by close friends and family.
Fraser, who has dual Australian and British citizenship, told news.com.au: "We've always wanted to get married so we decided to do it when Britain announced they were changing the laws. We had no idea we'd be the first."
They are delighted with their marriage but it will not be recognised by Australia, where gay marriage is not legal.
Same-sex couples in the Australian Capital Territory were briefly allowed to marry last year but the laws were overturned by the Australian High Court after just a few days.
It is the first time a same-sex marriage ceremony has been performed inside a consulate anywhere in the world and Sarah Midgely and Shirleen Robinson will be next up at the British consulate in Sydney on September 7.
Fraser added: "I hope that soon all Australians will be able to marry the person they love."