The move comes after the sport's governing body said Sri Lanka will be allowed to compete internationally both in bilateral cricket and global events once again following their recent suspension.
The ICC, however, stated that funding will be overseen externally and the upcoming Under-19 Men's Cricket World Cup will be moved to South Africa.
The suspension was initially announced earlier this month in the wake of government interference in Sri Lanka Cricket's (SLC's) administration.
Sri Lanka won just two of their nine matches at the Cricket World Cup in India and finished second bottom of the table, so did not qualify for the 2025 Champions Trophy.
A statement from the ICC said: "After hearing representation from SLC, the ICC board decided that Sri Lanka can continue to compete internationally both in bilateral cricket and ICC events after being suspended recently for breaching its obligations as a member in particular the requirement to manage its affairs autonomously and without government interference.
"However, funding to SLC will be controlled by the ICC and the ICC Board confirmed Sri Lanka will no longer host the ICC U19 Men's Cricket World Cup 2024, which will now be held in South Africa."
The U19 World Cup was originally scheduled from 13 January - 4 February 2024 and is likely to be played close to the same window.