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Abbas replaced Bangladeshi politician Mustafa Kamal in the largely ceremonial role, with the latter having resigned following the Cricket World Cup.
"This is the sport which has given us friendship, respect, recognition and an opportunity to serve our countries in different capacities. Personally speaking, it has given me more than I can ever possibly repay," Abbas said in a statement on the ICC's website.
"I am thankful to all of you for the support and confidence placed in me by confirming my nomination. I am also grateful to the PCB [Pakistan Cricket Board] for proposing my candidacy as the ICC president. I assure you all that I will stand shoulder to shoulder with all the ICC Members as we continue to strive to inspire more and more people to fall in love with the game we cherish."
Abbas played 78 Tests for Pakistan between 1969 and 1985, scoring 5,062 runs at an average of 44.79.
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On the third day of the ICC's annual conference, Serbia's application to be an affiliate member was approved, while Morocco and Turkey's memberships were suspended and Brunei was removed altogether.
That left the ICC with 105 members.