So far no further details have been revealed about the new addition.
News broke in June that Jamie and Amelia, who performs under the name Slow Moving Millie, were expecting their first baby together.
Amelia has been in safe hands throughout her pregnancy. Jamie's father Jim and his step-mother Samina are respected gynecology and obstetrics consultants in his native Northern Ireland.
It is understood that Samina gave Amelia her very first scan, before confirming the pregnancy to Sunday Life.
"Jim and I are delighted that our third grandchild is on the way," she said. "The early well-being scanning was a beautiful and emotional experience for all present."
Jamie, who previously dated Keira Knightley, married Amelia in a romantic ceremony at a country house in Somerset in April of this year.
He is currently hard at work in Canada filming alongside Dakota Johnson. It is thought that Jamie, Amelia, and their newborn son, will spend their first Christmas in a rented property in Vancouver, where they have temporarily set up home.