The 42-year-old American actor and 31-year-old Russian model welcomed a baby girl they named Lea de Seine Shayk Cooper, according to E! News.
News Cooper and Shayk were expecting broke in November after the model was spotted with a slight baby bump during the 2016 Victoria's Secret Fashion Show. People reported Sunday that the model gave birth to a daughter two weeks ago.
"They are both extremely thrilled and feel so blessed," a source told E! after word broke.
Shayk was spotted with mom Olga Shaykhlislamov at a farmer's market Thursday in Los Angeles, and stepped out again over the weekend in Venice Beach. E! News reported in December that the model and Cooper plan to have more children.
"Bradley and Irina love each other so much and this is not gonna be the only kid -- there will be a few more after this one," an insider said. "Both families are very happy."
Cooper will reprise Rocket in Guardians of the Galaxy Vol. 2, and will also voice the character in Avengers: Infinity War. Shayk is known for her modeling work with Victoria's Secret and Sports Illustrated.