The pair, who have been together for nine years, revealed the sad news in a joint statement to People yesterday evening (14 May).
In the statement, they said: "It is with tremendous sadness that we have come to the decision to divorce."
It went on to explain: "We enter this next phase with friendship, love and respect for one another and the shared focus of caring for our son."
James,37, and Anne-Marie,45, first got together after meeting on the set of TV show Shameless, which they both appeared in.
Since then, Scottish James has gone on to do Hollywood flicks, including the new X-Men: Apocalypse, while Anne-Marie has also starred in various blockbusters, including last year's Suffragette.
The stars got hitched back in 2006 and Anne-Marie gave birth to their son, Brendan, in 2010.
They also requested in the statement: "We ask that you respect our and, most importantly, our child's privacy during this time."