The Victoria's Secret model gave birth to the couple's first child almost a month ago. E! News learned of the news on April 9, the day she was spotted without a large baby bump in public, and learned they had welcomed a baby girl named Lea de Seine Shayk Cooper.
A source told E! News exclusively Wednesday that being a mother "feels so natural" to Shayk.
"She is such a loving and caring mom," the source said. "She is in bliss. Life is good. She can't keep her eyes off her little girl."
"Bradley is filming [A Star Is Born] now but still is making time for his baby," the source added. "He is just in love. They are both very protective over their baby and are only letting a few close family and friends to see their baby. Irina's family is in town and is helping with the baby. She has help as well around their home."
The source also said Shayk "wants more kids." Another insider had told E! News in December that both the model and Cooper hope to have more children.
"Marriage is in the cards" for the couple, the first source told E! News, but they "are not rushing" towards the aisle.
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Shayk and Cooper have not commented on their new arrival. The model has never posted a photo of her baby bump on social media. On Wednesday, she shared a photo showing herself lying on her back on a float in a pool while wearing a bikini. It is unclear when the pic was taken, although she captioned it "Pre-sunset #currentsituation."
"When Irina had her baby she lost most of the unwanted weight right away," the source told E! News. "She has great genetics."
Shayk also waited about a week after giving birth and then "went hard" with her workouts, the source said.
"She has done a mix of cardio, weights and eating really clean," the source explained, adding that the model has been "staying away from fatty foods," except for "cheat days" and has been "doing everything in moderation."
"She has been working with Bradley Cooper's trainer as well as a few other fitness gurus that been helping her," the source added. "Bradley and Irina have many things in common and fitness is one thing. They both work out together and take care of themselves. She has jobs that are coming up that she is contracted for soon, so getting back in tip-top shape is a priority."