"I'm engaged!" People.com said Hudson told "Today" interviewer Matt Lauer. "It just happened a week ago. I'm so glad you noticed [my ring]. I haven't really announced it. … I was waiting for someone to notice."
People.com said the "Almost Famous" and "Something Borrowed" star was tight-lipped about how Bellamy proposed to her, other than to say: "It was very sweet. It was very romantic."
The couple have been dating for about a year.
UsMagazine.com said the marriage news comes as something of a surprise since Hudson said in January: "I don't feel it necessary to get married ... I already have one child, and have had one divorce, so it is not necessarily the golden ticket. I just want to be happy."
Hudson, 32, was previously married to rocker Chris Robinson. They have a 7-year-old son named Ryder.