The decision comes after a report by the UN cultural agency Unesco said the area "should be off-limits to commercial logging in its entirety".
The Tasmanian Wilderness covers about a fifth of the island and is one of the world's last big temperate forests.
Conservation groups have welcomed the Unesco report and the logging decision.
In 2014 the Australian government asked the agency to revoke the special status of the forest to open up parts of it to logging in order to boost the island's economy, where unemployment is above the national average.
But the move - by the government of former PM Tony Abbott - attracted much opposition from environmental groups.
The Unesco report released on Saturday said the organisation "does not consider a World Heritage property recognised for its outstanding cultural and natural values the place to experiment with commercial logging of any kind".
The Tasmanian Wilderness is home to ancient forests, some of the tallest flowering plants in the world and is a stronghold for several animals that are either extinct or threatened on Australia's mainland.
Both the Australian federal and the Tasmanian state government have said they will abide by that recommendation.

Nobel prize-winning geneticist Sir Paul Nurse told BBC Newsnight experts "are being derided and pushed back".
Mr Gove says he had economists mostly in mind when he said "people in this country have had enough of experts".
But he admitted some people may have felt "licensed" by his remarks to challenge all forms of expertise.
Mr Gove made the controversial remarks in an interview with Sky's Faisal Islam three weeks before last year's EU referendum.
Michael Gove was justice secretary at the time and a leading figure in the Vote Leave campaign.
Critics claimed Mr Gove was whipping up an anti-intellectual mood with parallels to Donald Trump's assault on media and other sources of information.
Mr Gove said his remarks were taken out of context because Mr Islam interrupted him before he was able to clarify that he was referring to "organizations with acronyms who had got things wrong in the past".
He told Newsnight he had failed to express himself more carefully because it was "a high profile, high intensity, high tension, high nervousness, encounter".
He insisted he did not regret using the word "expert" but added: "One of the things that is occasionally irritating is that people assume that what I was saying was a blanket rejection of facts, evidence, rigour - when in fact what I was trying to do was to say look let's simply not take arguments at face value, just because someone works for a prestigious organisation."
He conceded that some people may have felt encouraged by his comments to cast doubt on all forms of expertise. "It may be that there are some people out there who think that that I'm giving them licence to operate in that way. Who's to say?"
He added: "I would hope that people looking at my career would say whatever that phrase may have encouraged or licensed, actually the man uttering it was someone who believed in more knowledge and more critical thinking - not less."
But Sir Paul, a former president of Britain's top scientific body, the Royal Society, said even if Mr Gove had meant to cast doubt primarily on economics, he had been "irresponsible" not to clarify his remarks.
He said the comment "spilled over into all sorts of other areas where experts have an enormous contribution to make to the proper running of society".
"The fact that experts have been derided in this way does have an effect in undermining science and scientific evidence."
Sir Paul said the British public still has high levels of trust in scientists but we are living in a period where "opinion is on the front foot".
"Those who are expert, who have the knowledge, who have the intellectual ability to dissect these difficult problems, are being derided and pushed back," he said.
"My view about this is that it cannot last for very long, because opinion is not built on firm foundations and it rapidly falls apart. And I think we're seeing that already with, for example, Mr Trump.
"Science is built to last. Opinions are not built to last."
Ian Katz was reporting for BBC Newsnight. Watch his full report on experts on the programme at 22:30 on BBC Two - are catch up afterwards on iPlayer.
The Australian and Tasmanian authorities are abandoning their bid to have logging permitted in the Tasmanian Wilderness, a World Heritage site.
[NEXT_CONCEPT]
One of the UK's leading scientists says Michael Gove's attack on experts during the EU referendum risked undermining science and scientific evidence.