Harjinder Pal was arrested following the killing at their home in Southall, south-west London, in 2009 but was deemed unfit to be tried and was detained under the Mental Health Act.
A recent assessment of his mental health led to him being considered fit to stand trial at the Old Bailey court in London this week, where he admitted manslaughter on the basis of diminished responsibility.
His wife Kulvir Kaur, 21, who worked for a cleaning company in Southall, had an arranged marriage in India in 2008 with Pal, a policeman from Punjab, before the couple moved to England the following year.
On February 28, 2009, Pal strangled Kaur and dialled the emergency 999 number just after midday and told an officer he had "murdered" his wife.
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Police arrived to find Kaur's fully-clothed body in bed, with the covers pulled up to her neck and red marks around her throat.
Pal also told officers he had eaten rat poison found in the bedroom, the court was told.
Medical experts concluded Pal was suffering schizoid affective disorder, which meant he had delusional jealousy with no basis in fact.
"Only 16 days after moving in together, Kulvir was strangled to death in her bed by Pal. He claimed his motivation for the killing was his belief that his wife had been having affairs with other men," said Baljit Ubhey, the chief crown prosecutor for the Crown Prosecution Service (CPS) in London.
"These allegations were completely untrue and unfounded. The allegations caused great distress to Kulvir's family and have had a significant impact on their lives. I hope Pal's conviction and sentence provide some comfort to them," Ubhey added.