The measures taken to fix the damage will also have an important beneficial effect on climate change, as some of the gases that caused the ozone layer to thin and in places disappear also contribute to warming the atmosphere.
The ozone layer's increasing health has been put down to the 1987 Montreal Protocol - an global treaty banning ozone-depleting chemicals, including chlorofluorocarbons (CFCs), alongside new technology.
The decline in CFCs in our atmosphere as a result of those measures now mean the ozone layer is expected to have fully recovered sometime in the 2060s, according to the report by the UN Environment Programme, World Meteorological Organization, European Commission and other bodies.
The healing signs of ozone layer was revealed on Monday by a new assessment report on Montreal Protocol (MP), the over 30-year-old global treaty which deals with reduction of ozone-depleting substances.
This year, the ozone hole over the South Pole peaked at almost 9.6 million square miles - which is still about 16% smaller than the biggest hole recorded.
If nothing had been done to stop the thinning, the world would have destroyed two-thirds of its ozone layer by 2065, he warned. Without it, skin and eye damage can occur, and evidence suggests a rise in skin cancers associated with the thinning of the ozone layer.
At the recovery rates projected by the United Nations report, the northern hemisphere and mid-latitude ozone is scheduled to heal completely by the 2030s, followed by the southern hemisphere in the 2050s and polar regions by 2060.More news: Le'Veon Bell back in Pittsburgh but no word on meeting team
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'We are only at a point where recovery may have started, ' Mr Toon said.
"It's really good news", Newman said of the protective layer's recovery.
Recent reports have found that emissions of a banned CFC are increasing in China - something the Chinese government has vowed to crack down on. Newman said we'll need to ensure that the replacements for these gases don't worsen global warming.
The Montreal Protocol was finalized in 1987 in response to the realization that numerous chemicals used in aerosols, air conditioning systems, refrigerators, and industrial solvents were eroding the planet's stratosphere, creating a hole and allowing harmful levels of ultraviolet radiation to seep through the ozone layer.
But an amendment to the Montreal Protocol is set to come into place next year which will ban the chemical.
"I don't think we can do a victory lap until 2060", Newman told AP.
Erik Solheim, head of UN Environment, described the Montreal Protocol as "one of the most successful multilateral agreements in history". "The careful mix of authoritative science and collaborative action that has defined the protocol for more than 30 years and was set to heal our ozone layer is precisely why the Kigali amendment holds such promise for climate action in future".