A spokesman for the couple revealed the news saying: "We can confirm that Sam is pregnant with her and Aaron's first child. Both are very, very happy."
The artist-turned-film director and Aaron, 19, have been engaged since October after meeting and falling in love on the set of her directorial debut Nowhere Boy, charting the young life and rise of John Lennon.
Sam is already mum to two girls, 12-year-old Angelica and Jessie, three, from her 11-year marriage to art dealer Jay Jopling, which came to an end in September 2008.
Of her romance with Aaron, who takes the lead as the Beatles star in the silver screen biography, Sam has said that from the outset she felt the pair "had quite a psychic link".
And the 42-year-old, who has twice battled cancer, has dismissed the age-gap between them, saying: "I've always lived my life as fearlessly as possible."
"I really don't listen to other people's opinions, just follow my heart and my instincts."
It’s an attitude also adopted by Aaron – due to star alongside Nicolas Cage in action film Kick Ass later this year - "I'm an old soul and she's a young soul," he has said.
"We don't see an age gap, we just see each other."
After their engagement, the couple said that they were, for the moment, too busy to organise their wedding. And while it is not known when the baby is due, it looks like their plans may have to be put on hold a little longer.