In true Musk-style, the first photo of the baby was rather unusual, featuring a tattoo filter.
He joked: “Never too young for some ink haha.”
Musk shared the news of his son’s birth on Twitter this morning, writing: “Mom & baby all good.”
He had earlier said the baby was “a few hours away”. Musk has since replied to a Twitter user and said Grimes gave birth to a boy.
Grimes, 32, has been keeping fans updated throughout her pregnancy and in February revealed she had suffered “complications” and felt she was “woefully ill-prepared” to have a baby.
Later that month she told fans on Twitter she will allow the child to choose its own gender.
Musk and Grimes have been dating for more than two years and made their red carpet debut as a couple at the 2018 Met Gala.
South African-born Musk, one of the world’s most powerful and richest men, has five children with his first wife, the Canadian author Justine Wilson.
Musk has caused controversy in reason weeks, after calling for the United States lockdown to be lifted despite the country reaching 1m coronavirus infections.
The Tesla founder and multi-billionaire tweeted ‘FREE AMERICA NOW’.
Before his ‘Free America’ tweet Musk tweeted: “Give people their freedom back!” with a link to a Wall Street Journal opinion piece that suggests the lockdowns have not saved that many lives but have shattered local economies.
Musk later clarified that he did not think all shops and businesses should be reopened immediately.