The couple told Hello! magazine that they were "overwhelmed with happiness" at the birth of their son Elijah Joseph Daniel Furnish-John, who was born in Los Angeles on Friday to a surrogate mother.

"Both of us have longed to have children, but the reality that we now have two sons is almost unbelievable," they said.

The couple's first son Zachary was also born via a surrogacy arrangement in California in 2010.

"The birth of our second son completes our family in a most precious and perfect way," John and Furnish told the magazine.

"It is difficult to fully express how we are feeling at this time; we are just overwhelmed with happiness and excitement."

The "Candle in the Wind" singer, 65, has been in a relationship with 50-year-old film producer Furnish for almost 20 years and they have been in a civil partnership since 2005.

Last week the couple's spokesman denied reports they had become parents again, but they have often spoken of their desire for Zachary to have a sibling.

The baby shares his middle name, Daniel, with one of John's 1970s hits.