According to Mr Justice Singh said there was "no doubt" that Simpson-Kent should serve the rest of his life in prison.
Arthur Simpson-Kent, 49, stabbed Ms Blake to death along with their sons Zachary, eight, and Anon, four.
The Old Bailey heard he killed them when he learned Ms Blake was planning to leave him and take their sons away, BBC reports.
Sentencing him at the Old Bailey on Wednesday, Mr Justice Singh said there was "no doubt" that Simpson-Kent should serve the rest of his life in prison.
“The manner in which the defendant killed his victims in this case was truly horrific. Although the murder weapons have never been found, the evidence, including the pathology evidence, is consistent with his having killed each of his victims in turn, first Sian Blake and then each of the boys. It is consistent with his doing so with repeated blows with a blunt instrument, using severe force, and then by using a bladed weapon,” he added.
The court heard Simpson-Kent told psychiatrist Dr Philip Joseph "something just snapped in me".
"I felt as if I had just been pushed off a diving board and was falling."
Simpson-Kent said he grabbed a small axe that was in the kitchen before hitting her repeatedly on the head.
"My mind was blank and I was focusing on doing and not thinking. It was like I was there but not there," he said.
The judge, however, refused Simpson-Kent's claim that he was depressed and had planned on killing himself.
Arthur Simpson-Kent had arrived in Ghana in January 2016 after fleeing from the UK as a result of the incident.
He was arrested at Busua near Takoradi in Ghana on the 9th of January, 2016.
Arthur Sampson Kent later submitted himself voluntarily to be sent to the United Kingdom for trial.
He was arrested at Heathrow Airport after being extradited from Ghana.