The 49-year-old British actress and the American actor, also 49, left a Vogue bash hand-in-hand following the EE British Academy Film Awards in London, according to People.
Watts, who wore an all-black ensemble in support of the Time's Up movement, was all smiles as she led Crudup out of the party. Us Weekly reported in August that the pair started dating after meeting on the set of the Netflix series Gypsy.
"Naomi and Billy are dating, but in the early stages," a source told the magazine. "They're very into each other."
Watts split from Liev Schreiber in September 2016 after 11 years together. She shares two sons, 10-year-old Alexander "Sasha" Pete and 9-year-old Samuel Kai, with the Ray Donovan actor.
"I'm co-parenting. I'm doing okay," the actress said in the June issue of Vogue Australia.
"There are good days and bad days and Liev and I are on great terms and we're trying to do our absolute best for the sake of the children and we hope to keep moving forward in that way," she added.