The couple flew to the Seychelles on Boxing Day for a holiday with Law's three children by ex-wife Sadie Frost.
Frost, who split from the actor in 2003 after six years of marriage, said she was happy at the news.
"I'm delighted for Jude and Sienna and wish them all the best for the future," she told The Sun.
No date has been set for the wedding so far because of the couple's hectic work schedules.
Law and Miller met while filming the remake of Sixties hit Alfie.
"I just hadn't seen anything like it. I think she's extraordinary," Law said of the pretty blonde.
Miller said of her heart-throb boyfriend: "Sometimes I can't believe how handsome he is. I feel very blessed. I have had, and am having, such a lovely life."
Law is currently in the United States filming new movie All The President's Men, while Miller is back in London.
