"Les Miserables" star Bamber was absent when Madden scored a Golden Globe victory last weekend.
A source close to Madden has said: "They're both absolutely gutted but it was a decision made for the best. They were arguing almost daily towards the end and, despite considering couples' therapy, it became evident there were far too many issues that could not be fixed.
"Richard is the toast of Hollywood at the moment, and understandably wants to let his hair down. Ellie is a bit quieter, and wants to focus purely on her work. It felt like their day-to-day lives were increasingly becoming worlds apart."
"They were pretty inseparable from the day they met - and their friends and family had all merged - so obviously everyone around them is gutted too. But both Ellie and Richard hope to remain friends," the source added.