An independent review published in July found serious failings in the initial investigation into Colin Marr's death in July 2007 by Fife Constabulary.
Former senior CID officer David Swindle said in his report that Mr Marr's death was suspicious and should have been treated as such.
Mr Marr, 23, of Lochgelly, Fife, died from a single stab wound to the chest following an argument with his partner.
The new move came after Mr Marr's mother Margaret Graham and stepfather Stuart – who have challenged the police conclusion that his death was suicide – met Solicitor General Lesley Thomson and Crown agent Catherine Dyer yesterday. Local MSPs John Park and Willie Rennie, who lobbied for the private meeting, also attended.
Fife Constabulary said: "We note the decision and Fife Constabulary will co-operate fully with the Strathclyde Police investigation." Margaret Graham said she was relieved there would be a new investigation into her son's death.
"It's five years since he died from a single stab wound to the chest, and I hope this new investigation will lead us to establishing what went on that night in Lochgelly," she said.
"As a result of numerous mistakes by Fife Police we lost confidence in the force.
"We are pleased that another force will be investigating the case."
In his report, Mr Swindle recommended a review of fingerprint and forensic evidence, and the re-interviewing of five witnesses.
John Park MSP said: "It's welcome that there will be a new investigation into Colin's death. We had lost confidence in Fife Police's ability to continue this investigation after a number of failings since 2007."
Willie Rennie MSP said that, together with the family, "we simply want to establish what happened".
"It's been a painful saga for Colin's family but hopefully this new investigation will find the truth," he said.
Strathclyde Police said last night it would not be commenting on the move.
The independent review was conducted following a request by the Crown Office.
Mr Marr's girlfriend, Candice Bonar, said he stabbed himself in the chest with a kitchen knife at their home in Lochgelly after she accused him of cheating on her.
After a three-week fatal accident inquiry, Sheriff Alastair Dunlop said he could not decide if the death was suicide or homicide.
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