The 'Rolling in the Deep' star, who announced her pregnancy back in June, welcomed her son with partner Simon Konecki last week, The Mirror reports.
"Adele and Simon are ecstatic at their new arrival," a source said. "She was over the moon that they were expecting their first child together."
Konecki previously teased that the couple's baby is "coming so soon".
It was recently reported that Adele is renovating a home in Hove to live a low-key life with her new family.
"Neither she nor Simon wants to bring up the baby in London. They want to keep a low profile when the baby is born. I think we'll see even less of her then," an insider explained.
"Despite her millions, she is going to give the baby the most important thing of all - love. The baby is very special to have such a special lady as its mother."
A spokesman for Adele declined to comment on the reports, saying they have no plans to release a statement at this time.