CCTV footage showed him leaving the flat, after the attack at lunchtime on 13 September 2008, wearing a pair of the sisters' jeans and carrying a plastic bag.
Their bodies were found by the landlord two days later stripped to the waist, lying face-down on their beds.
He had been alerted by Yasmine's twin brother who was concerned the family had not heard from the girls.
Det Ch Insp Joanne Clews, of West Midlands Police, said it was the most horrific crime scene she had ever witnessed.
Sabrina, 19, had recently moved out of their family home in Wembley, London, to live with her older sister and was due to start a French degree in Birmingham.
Yasmine was an aspiring medical researcher and had met Ali in 2006 in a pub in Moseley, Birmingham, the court heard.
She spoke French, Arabic and English, as well as her native Berber, and had gained a place at the University of Birmingham to read chemistry.
She left after the first year and worked as a medical sales representative and a belly dancing instructor.
They were two "beautiful, talented, ambitious and determined girls who had their whole lives ahead of them," the family said.
Ali came to Britain from Baghdad in 1999 and claimed asylum. He was granted permanent leave to stay in the UK in 2004.
Ali and Yasmine had had an on-off relationship and Yasmine's flatmate Amarai Zidouk told the court that her friend had never smiled when she was with him.
Yasmine had tried to split up with him a few days prior to her death, because she felt Ali did not respect her.
"Yasmine's only mistake was her refusal to submit to such an abusive, vicious and evil individual," her family said after the trial.
Ali lost control and only recalls stabbing Sabrina twice in the flat
"Sabrina's [only mistake] was her brave attempt to stop this monster from killing her sister," her parents added.
Ali had spent five months in prison awaiting trial for 11 counts of rape and sexual abuse he allegedly committed against Yasmine in February 2008.
The case was dropped at the last minute because Yasmine said she did not feel able to give evidence about her ordeal in court.
Police said Ali's control over her was very strong and she was afraid of him.
Ali told the murder trial he had been provoked, but Det Ch Insp Clews said she doubted it and added that Yasmine had cried every time she mentioned the termination.
Ali was found guilty of two counts of murder by jurors at Birmingham Crown Court on Friday.
In a statement read by West Midlands Police on behalf of the sister's parents and three brothers, the family said: "We are relieved that the monster who took away our girls' lives in such a brutal and barbaric manner has today been found guilty of their murder.
"As parents and brothers of murdered Yasmine and Sabrina, sitting through this trial and having to watch and hear lies and denials from the defendant who has failed to show any kind of remorse for the pain and suffering he has caused, has been incredibly difficult.
"This verdict will not bring back our angels but it will ensure that this barbaric killer will be placed behind bars for a very long time, and that he will never get the chance to inflict any such suffering on any other family."
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