Frazer Neil, 25, choked Hannah Dorans with a dressing gown cord at the flat they once shared in Edinburgh.
Hannah, 21, had ended their four-year relationship weeks before the killing in February 2017.
Neil then became enraged when he discovered she was dating another man.
He later lured Hannah to the flat – but told jurors he had no memory of what happened.
Neil now faces a life sentence after he was convicted of murder at the High Court in Glasgow on Thursday.
The trial heard how the couple had met while they were both first aid volunteers.
They later moved into a flat in the Capital before getting engaged in 2015.
Despite claiming to be in love with Hannah, jurors were told of Neil’s “controlling” behaviour.
This included stopping her going on nights out, seeing friends and blocking people she knew on social media.
Jobless Neil also lived off Hannah’s wages from her care assistant’s job at a private hospital in Edinburgh.
Hannah’s dad Keith recalled how he ended up seeing “less and less” of his daughter.
He told the trial: “Near the end we were lucky if we saw her once a month. If Hannah was there, Frazer was there.”
But, in late January 2017, Miss Dorans appeared at her parents one morning.
Her dad said it seemed she had “fallen out” with Neil and had “had enough”.
The “final straw” was a glamping holiday Neil arranged that she was not happy about.
Mr Dorans said his daughter was “delighted at being free”.
But, Neil continued to hound his now ex. He told jurors this was in a bid to “reconcile” and “find out what went wrong”.
Prosecutors said he eventually “lured” Hannah back to his flat on February 11 2017.
He had got her there by with-holding paperwork she needed for a new car.
It was at the flat he murdered his defenceless victim.
Jurors heard a 999 call he went on to make in which a hysterical Neil states: “I’ve killed her. I didn’t mean to do it.”
But, in court, Neil claimed he could not remember what happened that morning.
He said: “In some way, shape or form Hannah died at my hands. I cannot bring her back.
“I would if I could in a heartbeat.”
But, in connection with the murder, he again insisted he had no memory of what occurred.
Neil insisted he “never” had an “intention to harm” Hannah.
He further denied being “jealous” after discovering Hannah had gone on a date with another man.
Jurors heard Hannah was found with a tie or cord from a dressing gown around her neck when police turned up.
Neil claimed he and Hannah had a shared interest in Fifty Shades of Grey-style sex games.
Prosecutor Alex Prentice QC said Neil had pulled it “so tight” Hannah could not breathe.
Mr Prentice: “You took the view that if you could not have Hannah, no one else could.”
Neil: “No, that is wrong.”
Mr Prentice: “You could not bear that Hannah wanted to leave you?”
Neil: “I struggled, yes.”
The court also heard Neil had got in contact with Hannah’s parents while on bail for the murder.
This was to “help arrange” her funeral.
Hannah’s mum Moira recalled feeling “numb” when she read the Facebook message.
Members of Hannah’s emotional family wept following the verdict.
In a statement issued to Police Scotland, Hannah’s family said: “Hannah was a much loved daughter, sister and auntie and we are absolutely devastated as a family by her death.
“We respectfully request privacy at this time as we try to come to terms with our loss.”
Detective Inspector Stuart Alexander of Police Scotland’s Major Investigation Team said: “My thoughts are with Hannah’s family who have had a long wait to see justice being done. This will not compensate for the loss of Hannah but I hope it gives them a degree of comfort at what is a very emotional time.
“During the course of the trial, Neil was shown to be a manipulative and dangerous individual who brutally took the life of a young woman who once trusted him.
“He continues to show no comprehension of the severity of his crimes and the devastation his actions have caused.
“To lose Hannah in such a way has caused indescribable pain to her family, friends and colleagues and my sympathies continue to be with them.”
Neil is due to be sentenced at Glasgow High Court on 29th November.
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