A violent argument erupted and Mr Brown, 69, was bashed repeatedly with a banjo before the neck of the instrument was rammed down his throat.
He died in hospital three days later after his life support system was switched off.
The defence case was that the accused, 31, was provoked by two unwanted sexual advances by Mr Brown, who was gay, and that attention, and the effects of his drink having been spiked, caused him to act in an involuntary way where he wasn't in control of his actions.
"Mr Ambach has spent eight years in prison. He has demonstrated extremely good behaviour. There have been no incidents of violence," the Parole Board decision said.
"Given the progress that Mr Ambach has made, the board does not consider him an undue risk to the community and parole will be granted. That will be for the purposes that he be deported to Hungary."