Grimes - who has rebranded herself as "c", the symbol for the speed of light - and Elon have been dating since 2018, and arrived together at the Met Gala that year.
The couple rarely discuss their relationship in public, but Grimes - whose real name is Claire Boucher - praised Elon as a "super-interesting person".
She said: "Look, I love him, he's great."
While Musk added: "I love c's wild fae artistic creativity and hyper intense work ethic."
In November 2017, Musk confessed he was looking for a long-term relationship.
He shared: "I'm not looking for a one-night stand. I'm looking for a serious companion or soulmate, that kind of thing."