Widely accepted for more than a decade as an accurate indication of ability, the key aspect of Dexter's system is that it takes account of the quality of opposition a player is up against.
Thus, unlike traditional averages, runs or wickets taken against Australia - the world's best side - count for more in the rankings than those taken against a weaker nation such as Zimbabwe.
In a statement ICC chief executive Malcolm Speed said: "The ICC has today (Wednesday) taken over ownership of the rankings produced by Ted Dexter Associates and sponsored by PwC.
"We have been looking to develop an official system of player rankings for some time and having studied a range of options we are of the view that these rankings provide the truest reflection of the relative merits of international cricketers."
Dexter, a dashing England batsman during the late 50s and early 1960s, whose company will continue to be involved in the on-going maintenance of the rankings, expressed his delight that the system had been officially recognised.
"I congratulate the ICC on their initiative in giving these rankings official status for the first time," said Dexter, also a former England chairman of selectors.
"It gives me great satisfaction to know that the cricketing public will continue to enjoy their interest in the continuously changing standings of all the best players in the world," the Sussex great added.
The rankings will now be sponsored by leading Asian electronic goods manufacturer LG.
1. Jacques Kallis (RSA) 2. Rahul Dravid (IND) 3. Ricky Ponting (AUS) 4. Brian Lara (WIS) 5. Damien Martyn (AUS) 6. Virender Sehwag (IND) 7. Sachin Tendulkar (IND) 8. Matthew Hayden (AUS) 9. Kumar Sangakkara (SRI) 10. Adam Gilchrist (AUS).
1. Glenn McGrath (AUS) 2. Muttiah Muralitharan (SRI) 3. Shaun Pollock (RSA) 4. Shoaib Akhtar (PAK) 5. Steve Harmison (ENG) and Anil Kumble (IND) 7. Jason Gillespie (AUS) 8. Makhaya Ntini (RSA) 9. Shane Warne (AUS) 10. Chaminda Vaas (SRI).
All-rounders (only five named):
1. Jacques Kallis (RSA) 2. Andrew Flintoff (ENG) 3. Shaun Pollock (RSA) 4. Sanath Jayasuriya (SRI) 5. Chaminda Vaas (SRI)
Test rankings (with points):
6. South Africa 100
One-day rankings (with points):
7. South Africa 101