Trounson beat his flatmate Russell Neil (17) to death with part of a wooden balustrade in Dunedin in 1990, Radio NZ reports.
Trounson, now 45, was a 19-year-old polytechnic student at the time he was sentenced, in 1991, to life imprisonment.
He has been released six times and been recalled on every occasion. He spent more than 10 months on the run from authorities in 2013.
Trounson would be supported outside the wire by an intensive reintegration support programme, the Parole Board said.
"Overall, there has been a positive shift in his behaviour and attitude since a long standing medical issue has been resolved," the board said in its decision released this morning.
"The principal factor leading to Mr Trounson's offending and all of his recalls has been the disinhibiting effects of alcohol.
"It seems that, at long last, he has shown that he can apply the lessons learned in the treatment and counselling he has engaged in since he has been in custody."
Trounson would remain subject to parole conditions for life and faced further restrictions - including a ban on alcohol and an order to notify his probation officer before entering any intimate relationships - for five years following release.
Trounson will appear before the parole board again in March 2018 to assess his release.
