The former professional boxer and her girlfriend, model Ella Baig, announced the news in an Instagram post posted on Tuesday 11 July.
The couple shared a black and white photograph of their hands cradling the baby’s feet on both their profiles, as well as another photograph of themselves smiling while Baig was in labour.
Adams wrote in the caption: “We are so excited to announce to the world that baby Adam has arrived.
“The first moment we laid eyes on you we felt an instant love and the strongest bond. We went to the moon and back to get you and we can’t wait to spend the rest of our lives watching you grow.”
In a separate statement to Hello magazine, 39-year-old Adams confirmed that the baby was born on Saturday 9 July.
“We are so excited to have welcomed our son into the world on Saturday morning at around 7am,” she said.
“Nothing prepares you for this moment in life but I am so overwhelmed with love and proud of Ella.
“We can’t wait to start this new chapter with baby Adams.”
The couple first announced that they were expecting in February, when they shared a photograph of their first pregnancy scan.
Speaking to The Independent in June, the sports star shared her hopes and fears for parenthood ahead of Adam’s birth.
She said: “I was a bit nervous. I guess I just thought my life was going to change forever.”
The former Strictly Come Dancing contestant added that one of the “scariest and hardest” parts about having a child will be “having to stand back and watch him fail so that he can pull himself back from that failure”.
She said that her and Baig’s hopes are for Adam to grow into an “understanding, really open-minded, confident, fun, kind, and happy” person.