The former couple -- and The Painted Veil co-stars -- have lived in New York for years with their sons, 8-year-old Sasha and 7-year-old Samuel.
"Over the past few months we've come to the conclusion that the best way forward for us as a family is to separate as a couple," the stars said in a joint statement.
"It is with great love, respect, and friendship in our hearts that we look forward to raising our children together and exploring this new phase of our relationship. While we appreciate your curiosity and support, we ask the press to be mindful of our children and respect their right to privacy."
"They have been on the rocks for quite a while," a source told People magazine.