Amal Clooney's Mother Baria Alamuddin Shops for the Twins in London

George Clooney's wife gave birth to a son and a daughter on June 6

Amal Clooney's mother is one excited grandma!

Baria Alamuddin has already started spoiling her twin grandchildren, Alexander and Ella, as E! News confirm she went shopping for them Tuesday just hours after George Clooney's wife gave birth.

The proud grandmother was photographed heading into E-Side, a family store in London that caters to modern organic living. We're told she purchased two sleeper onesies, a gray one with a bear print on it and another mint-colored one with rabbit print, which are both made of organic cotton.

Each ensemble also came complete with an adorable matching hat and bib (because, of course, these kiddos are bound to be fashionable like their mama).

"She made sure she had organic cotton made without pesticides and chemical free," a source told People of her purchases.

Meanwhile, George and Amal welcomed their twins into the world on Tuesday morning.

"This morning Amal and George welcomed Ella and Alexander Clooney into their lives," a rep told E! News shortly after Amal gave birth. "Ella, Alexander and Amal are all healthy, happy and doing fine. George is sedated and should recover in a few days."

News of the couple's pregnancy originally made headlines in early February thanks to Julie Chen, who confirmed on The Talk that the famous couple were expecting.

George—who is a first-time father at 56-years-old—confirmed the news himself in an interview a few weeks later.

"We are really happy and really excited. It's going to be an adventure," opening up about the news for the first time with French program Rencontres de Cinema. "We've sort of embraced it all…with arms wide open."

Congratulations again to the growing family!