Afghanistan's heroin trade remains strong
Burma, by contrast, remains on the US black list of drug-connected states for failing to uphold its international anti-drugs commitments.
Sanctions against Afghanistan were being lifted, Mr Bush explained, to allow the country to receive US aid.
Washington has strongly backed Hamid Karzai's interim government in Afghanistan since it emerged from the defeat of the Taleban.
The Bush administration has pledged about $300m in aid since the start of its military campaign to oust the Taleban on 7 October.
"It is in the vital national interests of the United States to provide the full range of US assistance to Afghanistan," Mr Bush said, announcing the waiver.
Afghanistan became the world's major heroin producer under the Taleban and the UN has warned that poverty is driving Afghan farmers to maintain their poppy fields.
Blacklist
Of the 23 nations on the US drugs blacklist, all but Afghanistan, Haiti and Burma were removed this year on the grounds that they were meeting anti-drugs standards.
But President Bush also waived anti-drugs sanctions against Haiti in view of its extreme poverty.
Burma remains on the list and is thus ineligible for US aid.
The US leader was required to identify any country on the list which had failed demonstrably to make substantial efforts against drug trafficking during the past year.
Previously, a president determined which countries on the list had cooperated fully with the United States, or taken adequate steps on their own, against drugs.
The change was brought about after complaints from Mexico and other Latin American states that the procedure was humiliating.