Yahya Babiker, 46, was found guilty at a trial last month of smashing his wife Randa Kamblawi's head with a hammer as their children slept next door.
He had claimed she fell in the bath and banged her head.
Members of Mrs Kamblawi's family attended yesterday's sentencing hearing at the High Court in Edinburgh, but learned nothing of the motive as Babiker continued to protest his innocence.
Lady Stacey told Babiker: "You have been convicted of the brutal and premeditated murder of your wife, who was the mother of your two young children.
"You have deprived her of her life and her children and her family of her. The testimonials and the plea in mitigation made on your behalf simply render your actions inexplicable."
The murder was committed on 19 or 20 October last year at the couple's home on Edinburgh's Nicolson Street.
Babiker, a shopfitter and a Sudanese national, and Mrs Kamblawi, 34, a student, had been married for eight years. On the afternoon of 19 October, Babiker was filmed on CCTV testing a crowbar and then buying a 3.99 claw hammer in a Homebase store. He returned home and attacked his wife as she lay in bed, hitting her at least five times with the hammer and fracturing her skull. He put her body in the bath, and took his two children to the home of a relative of his wife, saying she was tired and unwell.
Babiker intended fleeing to France and went to Edinburgh Airport, but did not have enough money for the one-way ticket to Paris. Instead, he took a flight to Heathrow and walked around London for several hours, while police in Edinburgh searched for him.
He returned north the same day, and handed himself in at a psychiatric hospital.
Babiker and Mrs Kamblawi were described as a normal couple who were active in Edinburgh's Sudanese community. Mrs Kamblawi's mother said her daughter was "a beautiful person who would help anyone."
The defence counsel, Herbert Kerrigan, QC, said a report on Babiker showed "a very favourable background" and a good relationship with his wife, although there was a period of separation.
Mr Kerrigan said: "In regard to the incident itself, I can offer little assitance. He (Babiker] maintains his innocence." make was that he was innocent,"