Ms Hall and the baby, weighing 8lb 3oz and named Gabriel Luke Beauregard Jagger, were doing fine, a spokeswoman for Jagger said.
Jagger, 54 is in Atlanta on tour with the Rolling Stones. He and Ms Hall already have three children - Elizabeth, 13, James, 11, and Georgia May, five.
He also has two daughters, Karis and Jade, from previous relationships. Jade, 26, the daughter of Jagger and former Nicaraguan partner, Bianca, has made the Stones' lead singer a grandfather twice over.
So newly-born Gabriel is already an uncle to Jade's children, Assisi, four and Amber, two.
Ms Hall, 41 and Jagger married on Bali, Indonesia, in 1990.
News of Ms Hall's pregnancy in June followed reports she had consulted divorce lawyer Anthony Julius - who represented Diana, Princess of Wales in her divorce settlement - after tiring of her husband's wandering ways. Jagger's name was linked with Pulp Fiction star Uma Thurman and the Czech model, Jana Rajich.
Stones' guitarist Ronnie Wood was quoted at the time as saying: "Jerry is not going to take any more. This time it really looks like it. She has known what's been going on for a long time, she's not stupid.
"She's known all about Mick's flings but she has been prepared to brush some of them, not all, under the carpet."
The impending birth brought the couple back together and Ms Hall agreed to patch up the relationship.
But the singer has yet to see his new son. He and the fellow Stones are touring the United States after releasing their 39th album, Bridges to Babylon, in September.
Jagger would fly back to Britain to see his new son when the tour ended on Friday, and should be at Ms Hall's side by Saturday, said a spokesman for the rock star.
The Stones' tour breaks this week and resume again in January.Reuse content