George & Amal Clooney Welcome Twins!!!

George and Amal Clooney are officially parents after she popped out twins ... a girl and a boy!

Their rep says the birth went down Tuesday morning ... and the lil Clooneys are named Ella and Alexander.

The high-profile couple had actually been keeping a low-profile lately in England. The last time Amal was out in public was at "The Promise" premiere on April 6 in London. You'll recall, George showed up to an event 20 days later in London ... with no Amal in sight.

Amal did throw George a surprise birthday party last month in London.

Their reps says mom and the kids are "healthy, happy and doing fine. George is sedated and should recover in a few days."

More like 18 years. Congrats!