Elton John And His Husband David Furnish, Welcome Their 2nd Baby Son Elijah Joseph Daniel Furnish-John. (See Photos)

Happy family: Sir Elton John and David Furnish proudly show off their second baby son, Elijah Joseph, who was welcomed into the world on January 11, 2013.

Tenderly cradling his new baby in his arms, Sir Elton John proudly shows off his family of four. Beside him sits husband David Furnish, and their two-year-old toddler Zachary.

The couple’s second son Elijah Joseph Daniel Furnish-John (to give him his full title) was born on Friday 11 January weighing 8lb 4oz.

Like his elder brother, little Elijah was born to the same California-based surrogate mother - whom the couple said they love ‘like a sister’.

They revealed that the boys are at least half-brothers as they share the same egg donor. But it is not clear if that is the same woman who carried them for nine months, or someone else.

Another unknown fact is which man is the baby’s biological father - if, indeed, either of them.

Neither Sir Elton, 65, or his civil partner Mr Furnish, 50, have revealed whether Zachary or Elijah carry their genes.

Another little Rocket Man! Sir Elton John and his partner David Furnish, pictured with son Zachary, two, welcomed Elijah Joseph Daniel Furnish-John into the world at 6.40pm on Friday

However on Zachary’s official birth certificate, Sir Elton is named as ‘father’ and Mr Furnish as ‘mother’ leading to speculation that the rock star is his biological father. They have also kept the identity of the boys’ surrogate mother a closely guarded secret.

Speaking to Hello magazine, Sir Elton said: ‘She is a wonderful, kind and loving woman, who we love like a sister. We have a very close bond with her and were in constant touch throughout the pregnancy, getting updates, seeing scans and sharing all the little details that make those nine months so exciting'.

Thrilled: The delighted pair said that the arrival of their second son, who was born in Las Vegas via a surrogate, 'completes our family in a most precious and perfect way.'

‘She has given us two amazing gifts and we in turn have a duty of care to her and are fiercely protective of her anonymity.’ 

Unlike elsewhere in the world, it is not illegal in California for a multi-millionaire such as Sir Elton to pay a significant sum of money to a surrogate or gestational carrier.

If she were paid, a surrogate mother could in theory have become very rich after successfully delivering first Zachary and then Elijah.

It is likely she would have signed a strict confidentiality agreement never to speak about the deal.

The couple said the arrival of their second son, who was born in Las Vegas, ‘completes our family in a most precious and perfect way’.

Doting dads: The couple welcomed first son Zachary into the world in December 2010

Sir Elton admitted that such was the intensity of love he feels for their firstborn, who was born on Christmas Day 2010, he was worried if he would ever be able to love another child as much.

‘But I have learned that a parent’s capacity for love is endless’ he said.

‘When another child is born, our depth of love just grows deeper and wider, so it was very emotional.’

Filmmaker Mr Furnish said: ‘Throughout our lives we have both loved and been loved, but the love of a parent for his or her child is different to anything else, as all parents will know. You find new depths of love, and experience pure joy.

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

‘The birth of our second son completes our family in a most precious and perfect way. It is difficult to fully express how we are feeling at this time; we are just overwhelmed with happiness and excitement.’ 

Sir Elton, who has sold more than 250million records in a four-decade music career, has previously regretted waiting so long for a child.

They had previously been turned down for adoption due to his age.

‘It changes everybody. It’s the most wonderful thing you could possibly go through,’ he said.

‘I regret a little bit that I didn’t do it sooner, but he [Zachary] has changed our lives. Everything is about him now.

‘He’s gorgeous, he travels brilliantly, he so loves people, and it makes our lives - he’s the icing on the cake.’ 

Their new son will want for nothing - if the example of his elder brother is anything to go by.

Zachary’s godmothers are Lady Gaga, magazine editor Ingrid Sischy, and Sichy’s partner Sandy Brant, while the couple spent thousands on his nursery and FedExing breast milk from his surrogate mother around the world.