It is the couple's first child who was born over the weekend, multiple sources confirm to People magazine.
The couple - 36 and 30, confirmed the news to the New York Post.
The 35-year-old first announced she was pregnant via a stunning photoshoot for Rodarte where she looked like an absolute Earth goddess.
In December rumors swirled that the Bring it On actress was expecting her first child.
Kirsten and Breaking Bad actor Jesse played a couple on the second season of FX's Fargo, which aired in 2015, and went on to become a real item the following year.More news: Summary of easyJet plc (LON:EZJ) Ratings
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Dunst opened up about her desire to start a family back in June 2017.
Dunst and her fiancé Jesse Plemons are said to have given birth to a healthy baby boy.
We honestly couldn't be happier for Kirsten and Jesse!
"I've been working since I was 3", she told the publication. "I love her so much", the Golden Globe nominee continued at the time.
'That love is just like... you can't experience that unless you have a kid'. I put her to bed last night and she woke up this morning and said to her mom, 'Where's Kiki?' I just love that.