Zimbabwe will now be able to take up their place in the ICC Men's U-19 World Cup in January and the ICC Super League later in 2020.
The ICC on Monday decided to readmit Zimbabwe and Nepal as its members following the conclusion of the Board meetings here.
Zimbabwe and Nepal were suspended in July this year following government interference in the running of the Board.
"I would like to thank the Zimbabwe Sports Minister for her commitment to the reinstatement of Zimbabwe Cricket. Her desire to work in support of Zimbabwe Cricket was clear and she has unconditionally complied with the conditions set down by the ICC Board," ICC Chairman Shashank Manohar said.
"Funding to Zimbabwe Cricket will continue to be on a controlled basis as part of a collective effort behind getting the game in Zimbabwe back on an even keel."
Zimbabwe will now be able to take up their place in the ICC Men's U-19 World Cup in January and the ICC Super League later in 2020.
Nepal has also been reinstated on a conditional basis following their 2016 suspension for breach of the ICC regulations which prohibit government interference and require free and fair elections.
Election of a 17-member Central Working Committee for the Cricket Association (CAN) of Nepal were completed earlier this month and paved the way for the re-admittance of the CAN.
"Given the progress made in Nepal, a transition plan will now be developed for the Cricket Association of Nepal to support full compliance with Associate Membership criteria, which will also involve controlled funding," Manohar said.
The ICC came to the decision after a meeting with the ICC Chairman and Chief Executive, Zimbabwe Cricket Chairman Tavengwa Mukuhlani and Zimbabwe Sports Minister Kirsty Coventry and Gerald Mlotshwa, the Chairman of the Sports and Recreation Commission.
In other decisions, ICC decided to increase the prize money for ICC women's events by USD 2.6 million.
The increase follows a rise in the revenue generated by the sport, a proportion of which is assigned to prize money.
For the ICC Women's T20 World Cup in Australia next year, the winners and runners up will now receive USD 1 million and USD 500,000 respectively -- five times the amount on offer in 2018.
An overall 320 per cent increase in the prize pot for 2020 (compared to 2018) will see every single one of the 10 competing teams receive significantly more as part of ongoing efforts to drive improved standards throughout the game and not just rewarding the top end.
There will also be a substantial increase in the money available for the ICC Women's World Cup 2021 with the prize pot increasing to USD 3.5m from USD 2m in 2017.
The Board also approved the establishment of an U-19 Women's T20 World Cup with the first edition to be played in Bangladesh in 2021 and every two years after that.
"We want to build a long-term sustainable foundation for women's cricket and that is about more than just prize money. It is about building a product that fans want to watch, that kids want to take up, that sponsors and broadcasters want to be part of," ICC Chief Executive Manu Sawhney said.
"Creating a Women's U19 event also improves the pathway available to young cricketers and ensures they have the same opportunities as their male counterparts.
"This significant increase in prize money and the introduction of a Women's U19 event is part of a much larger effort to grow the women's game around the world."
