The 31-year-old "Almost Famous" star has been dating the Muse frontman, 32, for nine months. She also has a seven-year-old son, Ryder, with ex-husband Chris Robinson, of US rock band The Black Crowes.
"It was not planned, but they are excited and embracing it," a source told the magazine. "She is happy for Ryder to finally have a brother or sister."
The news followed reports that the star's father, Bill Hudson, was writing a devastating tell-all book about his ex-wife, actress Goldie Hawn, Kate Hudson's mother.