Mulligan was nominated for an Oscar for her work in "An Education." She also starred in the films "Wall Street: Money Never Sleeps" and "Never Let Me Go."
Mumford leads the band Mumford & Sons.
"They're a great couple," a friend of the pair told UsMagazine.com. "Very sweet."
No details about how Mumford proposed or when the couple plan to exchange vows were immediately reported.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Penelope Cruz named 2013's 'Best Body' by Fitness magazine