The Men's T20 World Cup scheduled to take place in Australia this year will now be held in 2022, with next year's tournament remaining in India.
Australia was due to stage the showpiece in October and November, but the coronavirus pandemic put paid to that.
West Indies will instead look to defend their title in India in October 2021, with Australia hosting the tournament the following year.
The format for the 2021 edition will be unchanged, so the teams that qualified for this year's tournament will play in India and a new qualification process will take place for the event in Australia.
Due to the impact of the COVID-19 crisis, the Women's T20 World Cup in New Zealand has been put back from next year and will get under way in February 2022.
Five teams have already qualified for the event and they will still take their place in the tournament in 2022, and the three remaining places will be up for grabs in a qualification event next year.
ICC acting chairman Imran Khwaja said: "Over the last few months as we have considered how we return to staging global events, our number one priority has been to protect the health and safety of everyone involved in ICC events.
"The decisions the board have taken today are in the best interests of the sport, our partners and importantly our fans.
"I'd like to thank our partners at the BCCI, Cricket Australia and Cricket New Zealand as well as the Australian and New Zealand governments for their continued support and commitment to a safe return to ICC events."
ICC chief executive Manu Sawhney said: "We now have absolute clarity on the future of ICC events enabling all of our members to focus on the rescheduling of lost international and domestic cricket. We will now proceed as planned with the Men's T20 World Cup 2021 in India and host the 2022 edition in Australia.
"We have taken the decision to move the ICC Women's Cricket World Cup to give players from every competing nation, the best opportunity to be ready for the world's biggest stage and there is still a global qualifier to complete to decide the final three teams.
"There has been no women's international cricket played since the conclusion of the ICC Women's T20 World Cup earlier this year and due to the varying impact of COVID-19 globally that is likely to remain the situation for a number of the teams.
"Moving the event by 12 months gives all competing teams the chance to play a sufficient level of cricket ahead of both the qualification event and leading into a Cricket World Cup so the integrity of the tournament is maintained.”