Image copyright Antartica What does the ozone layer do?
At its worst in the late 1990s, about 10% of the upper ozone layer was depleted, Mr Newman said.
"If ozone-depleting substances had continued to increase, we would have seen huge effects".
Ozone is a colourless combination of three oxygen atoms kilometres above Earth's surface, it shields us from ultraviolet rays which cause skin cancer, crop damage and other problems.
The report said the source country or countries had not yet been identified.
This is due to internationally agreed actions carried out under the historic Montreal Protocol, which came into being over 30 years ago. "We stopped that", Paul Newman, a NASA scientist and co-chairman of the new United Nations report, told the AP.
The Protocol was in response to the revelation that chlorofluorocarbons (CFCs) and other ozone-depleting substances - used in aerosols, cooling and refrigeration systems, and many other items - were tearing a hole in the ozone layer and allowing risky ultraviolet radiation to flood through.
"Evidence presented by the authors shows that the ozone layer in parts of the stratosphere has recovered at a rate of 1-3 percent per decade since 2000", UN Environment and the World Meteorological Organization said in a statement. The Southern Hemisphere lags a bit and its ozone layer should be healed by mid-century.
The ozone layer starts at about 6 miles (10 kilometers) above Earth and stretches for almost 25 miles (40 kilometers); ozone is a colorless combination of three oxygen atoms.
The report also said it was the first time the hole in the ozone layer had shrunk in both size and depth and size since 2000.
As a result, in 1985 a gaping hole in the ozone over the South Pole was discovered.
The study, Scientific Assessment of Ozone Depletion: 2018, is the latest in a series of reports, released every four years, which monitor the recovery of ozone in the stratosphere.
However, while most of the banned gases have been phased out, the report found at least one violation of the protocol: an unexpected increase in production and emissions of CFC-11 from eastern Asia since 2012.
The Protocol is set to be strengthened in 2019 with the ratification of the Kigali Amendment which calls for the future use of powerful climate-warming gases in refrigerators, air conditioners and related products to be slashed.
On its own, the ozone hole has slightly shielded Antarctica from the much larger effects of global warming - it has heated up but not as much as it likely would without ozone depletion, said Ross Salawitch, a University of Maryland atmospheric scientist who co-authored the report.
Now scientists say the ozone layer is making a comeback and will make a full recovery in 42 years.
"I don't think we can do a victory lap until 2060", Newman told AP.