Presiding judge Justice Leighton Pusey, who handed down the sentence in the Home Circuit Court, has ordered that he serve 61 years and eight months before being eligible for parole.
Pusey highlighted, among other things, the brutal, vicious and serious nature of the crime.
It was also noted that Barnett breached the trust of his relatives and lacked remorse for his action.
The 23-year-old was convicted in July of five counts of murder in relation to the killing of his cousins Kemesha Wright, Kimanda Smith, 15, Sharalee Smith, 12, Rafaella Smith, 5, and 23-month-old Kishawn Henry Jr.
The victims were discovered inside their Cocoa Piece home in Clarendon with chop wounds and their throats slashed on June 21.
Barnett, who had been staying at the house, fled the area to Wilson Run in Trelawny, but was later apprehended in the parish.
At the sentencing hearing in September, Director of Public Prosecutions (DPP) Paula Llewellyn argued that Barnett, who pleaded guilty to five counts of murder, should get life in prison and should serve 60 years and nine months before being eligible for parole.
She had argued that the crime is one of the worst her office has seen in Jamaica.
The DPP's office had initially served notice that it was seeking the death penalty.
However, the request was withdrawn after Barnett pleaded guilty.
Barnett's lawyer Tamika Harris, however, asked the judge to give him a 33.3 per cent discount on the sentence.
She submitted that her client had saved the court's time and resources.
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