The couple released a statement which said they would continue to have "friendship, love and respect for one another" despite the separation.
They have a five-year-old son.
The statement read: "It is with tremendous sadness that we have come to the decision to divorce.
"We enter this next phase with continued friendship, love and respect for one another and the shared focus of caring for our son.
"We ask that you respect our and, most importantly, our child's privacy during this time."
The couple began their relationship when they starred as couple Steve and Fiona in the Channel 4 comedy-drama Shameless, which was later remade in the US.
McAvoy, 37, stars in X-Men: Apocalypse, opening later this month.
Duff, 45, recently starred alongside Carey Mulligan and Helena Bonham Carter in period drama Suffragette.