The 38-year-old Australian actress, who is best known for playing Billie in the Channel Ten drama alongside Asher Keddie, gave birth to son Archie Nicholas in a Melbourne hospital.
According to the Herald Sun, Stewart and her actor husband David Whiteley are "thrilled" with the new arrival.
A Ten spokesperson added: "Both Archie and Kat are doing exceptionally well."
In July last year, when Stewart was yet to announce her pregnancy, she said that motherhood was something she would "definitely want to do", adding: "I do love children. In five years' time, it would be nice to have a kid or two.
"I have a ridiculously adorable group of nieces and nephews. Being an aunty is good, [but] the reality is that the window shuts at some point. Any woman over 35 is conscious of that."
She has previously revealed that she "loves" her role in Offspring, saying: "The show gets better and better as time goes on. It's a bit left-of-centre and can be fabulously odd.
"I've had a run of characters that have been outspoken and badly behaved, and I relish that."
Last year, it was announced that the award-winning show will return to Australian television screens for a third season this year.
> 'Offspring' cast love "eccentric" show