Shia and Twigs, real name Tahliah Debrett Barnett, met while working on upcoming movie "Honey Boy", which the actor also wrote, and were linked romantically after the 32 year old was photographed leaving the musician's London home.
The new couple was snapped during a trip to a local grocery store, and while the stars didn't share any public displays of affection at the time, Twigs is said to have confirmed they are an item, telling the Daily Mail, "We're very happy. We're having a nice time."
Now the lovers have taken their relationship to Los Angeles, where they paused an outing in Studio City on Tuesday, November 06, to share a passionate kiss. The pair was even dressed similarly in matching white T-shirts and army green pants.
The romance is Twigs' first since calling off her engagement to "Twilight" star Pattinson in 2017 after three years of dating.
Meanwhile, Shia is in the midst of ending his two-year marriage to actress Goth, who he fell in love with while shooting "Nymphomaniac: Vol. II" in 2012.
They briefly split in 2015 after hitting headlines for a heated argument on the streets of Germany, but they soon reunited and LaBeouf proposed in early 2016.
They exchanged vows in an Elvis-themed wedding in Las Vegas in October, 2016, with just their mothers as witnesses.