The Hollywood actor, 32, was seen outside the house in London this week after meeting her on the set of a film this year.
The new romance comes after he reportedly split from actress Mia, 24, two years after they declared their love for one another at a commitment ceremony in Las Vegas.
Shia is said to have struck up a friendship with FKA Twigs while they worked on his new movie Honey Boy and they are now dating, according to the Mail Online.
The publication reports the singer, 30, who previously dated actor Robert Pattinson, confirmed the new romance.
She is believed to have said: "We're very happy, we're having a nice time."
The new couple were spotted together outside her house in east London as they headed off to pick up groceries.
Shia is believed to have ended his six-year relationship with Mia several months ago while FKA Twigs' romance with Pattinson came to and in 2017.
An insider told the Mail Online: "Everybody in their circle knows that Mia and Shia are separating…"
Mia met Shia on the set of the film Nymphomaniac and they were together for six years, but she's now believed to have moved out of the house they previously shared.
They even had a wedding-style ceremony in Sin City last year, but it was reportedly not a legal marriage.
FKA Twigs, whose real name is Tahliah Debrett Barnet, dated Twilight star Pattinson for two years and they were said to have been engaged prior to their split.
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