Holm, 25, proposed to Morton in Paris on Saturday, her 29th birthday. The Minority Report actress said in a statement Friday, "We're over the moon. We're very much in love and looking forward to spending the rest of our lives together."
The couple met about a year ago when Holm directed her in a video for the band The Victims. Morton's rep, Karon Maskill, says they will wed in September.
The best man will be Johnny Borrell, a singer with the band Razorlight.
Holm is the son of actor Sir Ian Holm, who played Bilbo Baggins in the Lord of the Rings movies.