In contrast to Mahathir's often controversial reign, the formal hand-over of power was performed with quiet dignity in a ceremony before King Tuanku Syed Sirajuddin at the royal palace in Kuala Lumpur.
Abd Allah, 63, took the oath of office as Malaysia's fifth prime minister since independence from Britain in 1957 as Mahathir, 77, followed through on a pledge to retire.
After Friday morning's ceremony the two men were due to travel separately to the prime minister's office in the new administrative capital of Putrajaya south of Kuala Lumpur.
Later in the day, Mahathir was due to clock out, using the punch card system he introduced for civil servants a month after becoming prime minister in July 1981.
And on Monday, Abd Allah will clock in after spending the weekend in his home state of Penang.
Malaysian newspapers published massive supplements of lavish praise for Mahathir on Friday, but he was snubbed by Australian Prime Minister John Howard and criticised by the United States Congress.
Howard said in a radio interview he had no farewell message for Mahathir, who has regularly dismissed Australia's bid to be accepted as part of Asia, describing it recently as "some sort of transplant from another region".
In Washington, the House of Representatives joined the Senate in condemning Mahathir for his remarks at an Islamic summit in mid-October that Jews rule the world by proxy.
Abd Allah Badawi is expected to
continue his mentor's policies
By a vote of 411 to 0, with one abstention, the lower chamber of Congress adopted a resolution condemning Mathahir's remarks as "incendiary" and "despicable".
Mahathir, 77, has acknowledged that his legacy was a controversial one.
'Mr Nice Guy'
Asked how he would like to be remembered, he said he did not mind if he was forgotten, but added: "They will not forget all -- as Shakespeare has said, 'the evil that men do lives after them, the good is oft interred with their bones'."
Mahathir's successor, Abd Allah Badawi, is known in Malaysia as "Mr Nice Guy".
But he will need more than charm to fill the big shoes left by Mahathir.
Within a year, probably much sooner, he will face an election, with his main opposition coming from the Islamist opposition.
However, Abd Allah has refused to be drawn on how he might try to change Malaysia when he takes over.
He has pledged to continue his mentor's policies, but there is no doubt the style will be different.
Mahathir is outspoken and confrontational while Abd Allah is seen as quieter, a team player.
Analysts say Abd Allah, who has no experience in economic management, is unlikely to change any of Mahathir's business policies which have brought dramatic growth to the country.
His regional foreign policy is likely to focus on enhancing political ties and trade with Southeast Asian nations and Japan, and it is possible he will be less critical of Australia, one of Mahathir's favourite whipping boys.
John Howard said he had no
farewell message for Mahathir
On the wider international stage he will probably find major trading partners in the United States and the European Union delighted to have a less prickly customer to deal with.
Domestically, analysts hold out little hope for improvement on human rights issues, for which Mahathir was regularly criticised.
As home minister, a title he held along with deputy prime minister, Abd Allah has over the past two years approved the detention without trial of scores of alleged Islamists.
Abd Allah's major legitimate political challenge will come from the opposition Islamic Party (PAS), a Muslim group which wants to introduce Islamic law.
Abd Allah has strong religious credentials, having majored in Islamic studies at University Malaya, but this is unlikely to impress the country's Muslims as long as he upholds the secular constitution.
Malaysia is sometimes described as the world's most economically successful Islamic state, and Abd Allah has made it clear he intends to keep it that way.