The couple have been together for three years, but Pattinson has ‘grown tired,’ according to reports.
A source told The Sun: “They were almost inseparable for their first two years together.”
But they are said to have ended amicably despite ‘drifting apart’.
The source continued: “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.”
The news comes months after Pattinson appeared to confirm they had got engaged.
The Twilight actor addressed the interest in his relationship with Twigs, real name Tahliah Debrett Barnett, during an interview with US host Howard Stern, who asked: “You're engaged, right?”
Pattinson replied: “Yeah, kind of.”
Speculation of a split first surfaced in August when Twigs was pictured without her engagement ring at Christopher Kane's London Fashion Week show.
A source at the time told E! that the relationship had been “fizzling out.”
“He is technically still with FKA twigs, but it doesn't seem like it will last,” they said.
“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.”
The famous couple were first pictured together in 2014. They rarely addressed their relationship in interviews and have only attended a handful of events together.
Twigs was subjected to a barrage of racial abuse when news of her relationship with Pattinson surfaced, something she said left her “genuinely shocked and disgusted.”
Standard Online has contacted representatives for Pattinson and Twigs for comment.