England and South Africa wanted tougher action on Zimbabwe
Zimbabwe have been persuaded to pull out of the ICC World Twenty20 to be played in England in June 2009.
The ICC has been discussing Zimbabwe's future at a board meeting in Dubai after England and South Africa broke off cricketing relations last week.
The sport's governing body has decided Zimbabwe will not, for now, be suspended from international cricket.
But that may change pending a fresh investigation of Zimbabwe Cricket by an independent ICC committee.
BBC cricket correspondent Jonathan Agnew said that committee would examine "every aspect of the workings of Zimbawe cricket, including the allegation that only members of [ruling party] Zanu-PF are eligible to play."
He added: "The findings of that committee will determine the long-term future of Zimbabwe Cricket, which could yet face suspension [at a later date] from the ICC."
Zimbabwe Cricket president Peter Chingoka said his country had voluntarily pulled out of the ICC World Twenty20, while the ICC said in a statement that Zimbabwe Cricket viewed the decision as a "one-off".
"Zimbabwe has agreed not to participate in the wider interest of cricket," Chingoka said.
"But we will continue to be a full member of the ICC and welcome any team that wants to play against us.
"We voluntarily agreed to back out of the World Twenty20 because we were told we won't get visas to England. We don't want to gatecrash where we are not welcome."
"By agreeing to withdraw from the World Twenty20 Zimbabwe have agreed to act in the interests of world cricket, thus avoiding the likelihood of that tournament being moved elsewhere and the added spectre of boycotted matches and possibly strikes by players."
Secretary of state for Culture, Media and Sport Andy Burnham said he would have liked to have seen tougher action against Zimbabwe.
"I welcome the fact that Zimbabwe will not play in the World Twenty20 in England next year," he said.
"The Government made it clear that, in the current circumstances, the team whose figurehead is Mr Mugabe would not be welcome.
"While I would have preferred the ICC to take a stronger stance against Zimbabwe cricket, this solution still allows individual cricket authorities to make their own choices over whether to play Zimbabwe."
Prime Minister Gordon Brown said he welcomed the decision: "This will allow the Twenty20 tournament in England to go ahead.
"It also sends a powerful message to Zimbabwe that the Government must change or face further isolation."
We're grateful the ICC saw the point of view we held
ECB chairman Giles Clarke
The England and Wales Cricket Board (ECB) said last week it would not welcome Zimbabwe's cricketers because of the close links between Zimbabwe Cricket and the regime of president Robert Mugabe.
This was after Cricket South Africa broke off relations with their near neighbours because of the political situation in the country.
The ECB is now assured a welcome financial windfall from hosting the ICC World Twenty20, and ticket sales are already progressing well.
ECB chairman Giles Clarke said he was satisfied with the outcome of the meeting in Dubai.
"This matter led to a complex and lengthy series of negotiations," Clarke told BBC Radio 5 Live.
"We've had long discussions with our colleagues on the ICC over the last three days and we're grateful they saw the point of view we held."
ICC president David Morgan and general manager Dave Richardson
An ICC spokesman confirmed Zimbabwe's full member status of the organisation had not even been discussed at the Dubai conference.
The spokesman, James Fitzgerald, added: "We don't live in a vacuum. People can see what's going on and politicians are making political decisions based on the political situation in Zimbabwe.
"As a sporting organisation, we make decisions based on cricket and even if we wanted to it's unlikely political considerations are at the forefront."
The qualifying event for the ICC World Twenty20, in Belfast in August, is likely to produce three extra teams to go through to next year's finals.
Before Zimbabwe's withdrawal, that tournament would have produced just two qualifiers out of Ireland, Scotland, Bermuda, Kenya, the Netherlands and Canada.
The ICC's cricket operations department will confirm the new qualifying process in due course.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.