They share a daughter named Marlowe who was born in 2012, reported Ace Showbiz.
The breakup report came after their recent vacation together in Spain.
"They were in a bit of a rough patch for awhile. Their schedules on top of raising a child started to get to them," a source said.
Miller, 33, started dating Sturridge, 29, in 2011 and got engaged a year later. It was the first marriage for both. Before seeing Sturridge, Miller was previously linked to actors Jude Law and Balthazar Getty.
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