The pair are said to have “drifted apart”, with the break up being “amicable”.
Speaking to The Sun, a source explained: “Rob is tired of it, has called off their engagement and told friends they have split. With so much history between them, though, there are still strong feelings there.
“It’s a difficult situation but things have become tough between them for some time and they both know they were no longer working as a couple.”
Speculation that all was not well between Robert and Twigs, real name Tahliah Debrett Barnett, first surfaced in August when the musician was pictured at Chrisopher Kane’s London Fashion Week show without her engagement ring.
At the time an insider told E! that the romance is “fizzling out”.
They said: “He is technically still with FKA twigs, but it doesn’t seem like it will last.
“They were serious at one point, but not anymore. The whole thing with Rob saying they are ‘kind of engaged’ speaks for itself. The relationship has been fizzling out.”
Throughout their three-year romance the celebrity couple were incredibly private, rarely speaking about one another in interviews and only attending a few showbiz events together.
Their relationship previously hit the headlines after Twigs revealed that she had been subjected to hateful, racist abuse from Robert’s fans after they first went public, saying that she had been left “genuinely shocked and disgusted” by the vile remarks.
Yahoo Celeb UK have contacted Robert and Twigs’ reps for comment.