"Ruth and Jake were all over each other and didn't seem to mind who saw them," a source told The Sun newspaper.
The source added: "They were holding hands and shared a little kiss, it was sweet."
The pair are starring together in Constellations, a love story centered around one couple but based in various parallel universes.
Jake and Ruth have been spotted spending time together over the last few months, and there were reports that the two were seen kissing in New York in December.
The British actress, who starred in BBC drama and won her first major award for her role in US drama The Affair, sat with Jake and his sister Maggie Gyllenhaal at the annual awards show, and the two later cosied up to one another on the red carpet for the premiere of Constellations.
It would be Jake's first relationship since he split with model Alyssa Miller in 2014. He had previously dated Taylor Swift for a few months, after which the pop star wrote many of her tracks for the album Red.
Ruth was previously in a long-term relationship with Jude Law, although the pair never officially confirmed their status.