Rooney, 35, had previously not confirmed her pregnancy but was seen with a baby bump over the summer.
The happy news was announced by Victor Kossakovsky during a question-and-answer session at the 2020 Zurich Film Festival after a screening of Gunda, a film Joaquin, 45, worked on as executive producer.
Apologizing for Joaquin’s absence from the festival, Kossakovsky said, “He just had a baby, by the way, his name was… a beautiful son called River, so he can’t promote him now. “
Baby River is believed to have been born a month ago.
Rooney and Joaquin met when they worked together on the 2013 movie Her.
But they didn’t start dating until three years later.
They also starred in Don’t Worry, He Won’t Get Far on Foot, Dominion and Mary Magdalene together.
The couple confirmed their engagement in May last year, but have yet to get married.
Oscar winner Joaquin said he initially thought Mara “despised” him.
“She’s the only girl I’ve ever looked for on the internet,” he told Vanity Fair last October.
“We were just friends, email friends.
“I had never done that. I have never searched for a girl online. “