The couple broke the news of the birth of Zachary Jackson Levon Furnish-John, on December 25 in California, to UsMagazine.com.
The baby weighed 3.6 kilograms and measured 56 centimetres.
The identity of the birth mother was being withheld. It is also not known which of the two men is the child's biological father.
'We are overwhelmed with happiness and joy at this very special moment,' John and Furnish said in a joint statement. 'Zachary is healthy and doing really well, and we are very proud and happy parents.'
The boy is the first child for John, the 63-year-old multi-millionaire singer and rock legend, and Furnish, 48, a Canadian filmmaker.
The couple have been together since 1993 and became the first celebrity gay couple to be married in a civil union in England when such partnerships were legalised in 2005.
Actress Elizabeth Hurley, a long-term friend, was among the first to offer her best wishes. 'Massive congratulations to David and Elton on having their beautiful son. Can't wait for my first cuddle,' she wrote on the social networking site Twitter.
John sought in 2009 to adopt a boy while visiting an AIDS orphanage in Ukraine, but his request was denied because of laws requiring adoptive parents to be under 45 and married. Civil unions did not qualify under the law.
John revealed last year that the couple had often discussed adoption, but that he had been reluctant to go ahead with it because of his age.
But it was the death of his long-term keyboardist, Guy Babylon, that helped changed his mind, reports said. Babylon, who died of a heart attack aged 52 last year, had two children whom the singer described as 'wonderful.'
'What better opportunity to replace someone I lost than to replace him with someone I can give a future to?' John said at the time.
However, he and Furnish are not the first celebrities to opt for surrogate parenthood. Sex And The City star Sarah Jessica Parker's twin daughters, Tabitha and Marion, were born via a surrogate last year.
While surrogacy has increasingly become an option for gay couples in Britain over the past decade, it remains tightly regulated under British law. Couples often consider travelling abroad, where the rules are less strict.
California is recognized as being generally accepting of surrogacy agreements, including those that involve gay and lesbian parents.
Under Britain's 2008 Human Fertilisation and Embryology Act, the birth mother of a child born through a surrogacy arrangement is always considered the legal parent until this is changed by the courts.