According to the BBC Newsbeat, Voici printed the pictures on Friday, claiming they were the first images of Ella and Alexander.
The magazine explained the publication of the photographs by a “public demand.”
The actor said in a statement: “Over the last week photographers from Voici magazine scaled our fence, climbed our tree and illegally took pictures of our infants inside our home.”
George and Amal Clooney welcomed twins Ella and Alexander in June. The couple haven’t released any photos of them.
According to the edition, they were at their home in Lake Como, Italy, when the Voici photos were taken.
George Clooney released a statement condemning the magazine for publishing the grainy shots on its front cover.
“Make no mistake, the photographers, the agency and the magazine will be prosecuted to the full extent of the law. The safety of our children demands it,” he said.