Bill Gates is still hopeful the world will be "completely back to normal" by the end of 2022.
Speaking to Sophy Ridge On Sunday, the entrepreneur and philanthropist added the US should soon have excess coronavirus vaccines to share with other countries.
But the 65-year-old said he was worried the world would not learn the lessons of the COVID pandemic to prepare for future global disease outbreaks.
He was also critical of the cuts which have been made to the UK's aid budget, which has fallen from 0.7% of gross national income to 0.5%.
Asked by Sky's Jayne Secker if he was hopeful the world would be "completely back to normal" by the end of 2022, Mr Gates said: "Yes, I am."
He went on: "There are still some questions about how broadly the Johnson & Johnson vaccine will get used, if that's accepted it would be very beneficial but some of the rich countries including the US and the UK, even this summer will get to high vaccination levels and that'll free up so that we're getting vaccines out to the entire world in late 2021 and through 2022 and so, we won't have eradicated this disease but we'll be able to bring it down to very small numbers by the end of 2022."
Mr Gates, who made his billions with technology company Microsoft, said there was inequality in vaccination rates around the world.
He said: "We don't have world government that sits there and ignores the US research & development money or UK R&D money and overrides that.
"Because the fact of getting elderly people vaccinated in the rich countries, which actually had the pandemic worse than most of the developing countries, that was a good thing.
"The fact that now we're vaccinating 30-year-olds in the UK and the US and we don't have all the 60-year-olds in Brazil and South Africa [vaccinated], that's not fair, but within three or four months the vaccine allocation will be getting to all the countries that have the very severe epidemic."
Speaking on his concerns for the future, Mr Gates said he is worried the world will "forget about" COVID and will not use it to ensure better preparedness for future pandemics.
However, the billionaire thinks that because "trillions were lost" financially, "this generation will remember" and look at how a global response to a similar crisis can be coordinated.
During the week, Dominic Raab, the foreign secretary, confirmed that the government was cutting foreign aid to 0.5% from 0.7%, in a move criticised by charities.
Mr Gates said: "The quicker the UK can get its aid level back up to the 0.7% the better. The needs there are dramatic, UK aid - the voters there should be very proud of the impact that that has.
"It's been the strongest proponent of getting behind vaccines and making sure we eradicate polio and with the cutbacks we won't be able to do as much so I hope that gets restored because it is of critical importance."
In his statement, Mr Raab said the UK would "return to our commitment to spend 0.7% of gross national income on Official Development Assistance when the fiscal situation allows".