George and Amal Clooney Welcome Son Alexander and Daughter Ella

George and Amal Clooney have welcomed twins!

“This morning Amal and George welcomed Ella and Alexander Clooney into their lives. Ella, Alexander and Amal are all healthy, happy and doing fine. George is sedated and should recover in a few days,” the new parents of two say in a statement.

Born at St. Mary’s Hospital in London, Alexander arrived first, at 12:54 p.m., followed by Ella at 12:56 p.m., according to birth certificates obtained by PEOPLE.

A source close to the couple’s family tells PEOPLE, “This is very good news. We’re very, very happy. George is going to be a great father of twins.”

Amal’s boss, Geoffrey Robertson QC of Doughty Street Chambers, also tells PEOPLE he is elated for the couple: “All I can say is that it’s a great co-production.”

Sources confirmed in February that the Oscar-winning actor-director and the international human-rights lawyer were expecting. George, 56, Amal, 39, and their families are “all very happy,” a source said at the time.

The two-time Sexiest Man Alive — and first-time father — opened up for the first time in late February about having twins on the way, saying with a smile during an interview with Laurent Weil on his French program Rencontres de Cinéma,“We are really happy and really excited. It’s going to be an adventure.”

Added the then-dad-to-be, “We’ve sort of embraced it all … with arms wide open.”

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Matt Damon spoke up soon after the news broke about his longtime pal becoming a father, telling Entertainment Tonight Canada, “I was working with him last fall and he pulled me aside on set and I mean, I almost started crying. I was so happy for him.”

The Clooneys wed in September 2014 in Venice, Italy, surrounded by loved ones. The star-studded list of around 100 guests included friends such as Damon, Cindy Crawford, Emily Blunt and Bono.

Following the glamorous weekend nuptials, George told PEOPLE that being married “feels pretty damn great.”

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Since the news broke, the couple have stayed relatively private about Amal’s pregnancy.

The human rights attorney made her first event appearance following the news in late February, when she accompanied her husband to the 42nd César Awards in Paris. Amal wore a white strapless fitted sheath dress featuring an ombré feathered bottom, her baby bump just visible under her ensemble.

“It is a great honor for us to be here. It’s the first time we’re in Paris together so it’s a bit of a romantic weekend for us,” she told French reporters at the time.

Following the pair’s date night at the prestigious event, they were spotted shopping at the Parisian family-run furniture showroom Baudou, where a staffer told PEOPLE the “very friendly and very, very elegant” Amal was “looking exclusively at cribs and nursery furniture.”

In March, the high-profile attorney visited the United Nations to deliver a profound speech, calling for the Iraqi government‘s investigation into genocidal crimes committed by ISIS.

Later that month, Amal stepped out in London to participate in a discussion about international crimes in Iraq and Syria at Chatham House, the Royal Institute of International Affairs. The then-mom-to-be opted for a long-sleeved red dress and knee-length beige coat over her growing bump.

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George and Amal have spent a good deal of time in England, being snapped multiple times near their countryside mansion west of London — where they have been quietly nesting in preparation for their twins‘ arrival.

George admitted naming wasn’t exactly his strong suit, joking to Entertainment Tonight in March in reference to his tequila company, “My wife says I can’t name [the twins] Casa and Amigos. That’s the one thing I’m not allowed to do.”

Crawford and her husband, George’s Casamigos business partner Rande Gerber, used the opportunity to poke a little fun at the actor, gifting him and Amal with two onesies reading “CASA” and “MIGOS.”

Luckily, the star did have one skill down pat: “I know swaddling,” he told Extrain March. “I know what I’m in for.”

In all seriousness, the Ocean’s Eight star was “excited but nervous” about becoming a first-time dad, a source close to the couple’s inner circle told PEOPLE in February.

“He is excited about the kids, but also has the normal amount of nerves that come with being parents,” the source continued.

Added another insider, Amal “strikes me as someone who’ll be a fantastic mother. Intelligent, loving, funny, smart, nurturing. She doesn’t seem someone who will let kids get away with being Hollywood children.”

A source on the set of George’s recent movie Suburbicon told PEOPLE the star, who hadn’t yet revealed the pregnancy news, hinted that he was going to take some time off work.

“That would be very rare for him, but now it all adds up,” the set source said. “He’s going to be the best dad.”

• With reporting by PHIL BOUCHER and PETER MIKELBANK