ICC president Ehsan Mani said the decision was confirmed by a vote of the ICC executive board because of the exceptional nature of the matches in which players from all ICC full member countries are available to play.
The first of the two appeal games takes place at the Melbourne Cricket Ground on Monday between Asia and the Rest of the World with the second to be staged in Asia next month or March.
"The ICC board is of the view that due to the extraordinary circumstances that have brought about these two matches an exception to the existing rules should be made," Mani said in a statement released here on Friday.
"This decision applies only to these two matches and does not change the status of other One-day matches from the past or in the future."
The ICC World XI will include top players from Australia, England, New Zealand and the West Indies while the Asian Cricket Council Asian XI will include leading players from Bangladesh, India, Pakistan and Sri Lanka.
The proceeds from the match in Melbourne will be donated to the global relief and development organisation World Vision, the ICC said.
The number of people killed when an earthquake and tsunamis devastated Indian Ocean coastlines on December 26 shot up past 165,000 Friday.