Thurman, who is best known for her roles in "Pulp Fiction" and "Kill Bill," was previously married to actors Gary Oldman and Ethan Hawke. Thurman and Hawke are the parents of two children, while Busson also has two children with his ex-girlfriend, model Elle Macpherson.
"I can confirm she is engaged," Stephen Huvane, Thurman's representative, told People.com Friday.
A source also told the entertainment news Web site Busson gave Thurman an eight-plus-carat center diamond surrounded by 20 smaller stones when he proposed.
"It's the most beautiful piece I've ever seen," the insider told People.com. "Arki did a wonderful job."
The couple has been dating since last summer.
A date hasn't been announced for the wedding, the report said.
Celebrity Families of 2014 [PHOTOS]