The film is inspired by 1980s TV series of the same name and stars Gosling as Colt Seavers, a top Hollywood stuntman down on his luck after an on-set accident
His ballet dancer girlfriend gave birth to a son in New York on Thursday, his publicist said.
"Melanie Hamrick & Mick Jagger’s son was born today in New York and they are both delighted.
"Mick was at the hospital for the arrival. Mother and baby are doing well and we request that the media respect their privacy at this time," Fran Curtis, the long-time publicist for the Rolling Stones, said in a statement.
The 73-year-old singer already has seven children with previous partners, as well as five grandchildren, and he became a great-grandfather in May 2014.
Jagger and Hamrick, 29, began dating about two years ago, according to media reports.