According to a source, George and Amal, who welcomed the twins last month, are enjoying parenthood and things are "going great" for the family.

"Everything is going great with the babies. (George and Amal) are happier than they have ever been and really enjoying being parents ... They are truly in love and just want to be with the babies and not do much else," the source told eonline.com.

"This (Tuesday) morning (we) welcomed Ella and Alexander Clooney into (our) lives," the Clooneys told Page Six in a statement. "Ella, Alexander and Amal are all healthy, happy and doing fine."

They jokingly added that the first-time father "is sedated and should recover in a few days".

The pregnancy news broke in February on the TV show "The Talk," when host Julie Chen revealed that Jay Z and Beyonce weren't the only ones expecting twins and then congratulated the Clooneys. 

In a video address at the awards ceremony of the Aurora Prize for Awakening Humanity, held on May 28 in Yerevan, Armenia, the Oscar-winning actor, said: "I really would have been (in Yerevan) but if I came there and my wife had twins while I was there, I could never come home."

Clooney's wife, Amal, an international human rights lawyer whom he married in 2014, is due to give birth in June.