The former Citibank executive bagged 76,161 votes against 29,443 for his main opponent in Attock district of central Punjab province in Wednesday's poll, where he narrowly survived an attack on 30 July, an election commission official said on Thursday.
His driver and eight others were killed in the attack that officials have linked to Usama bin Ladin's al-Qaida network, which is bent on deposing President Pervez Musharraf for his support for the US-led so-called War on Terror.
Aziz, 55, whom Musharraf picked to be prime minister in June after the abrupt resignation of the incumbent, also trounced his opponent in a second by-election in Tharparkar in Sindh province by securing 152,102 votes against the rival's 10,732.
"I will try my level best to improve the life of country's common man and make efforts to maintain peace and harmony in the country," the official APP news agency quoted Aziz as saying.
Information Minister Shaikh Rashid Ahmad told reporters Aziz would form a new government next week. "I expect a new government to be formed between the 22nd and 25th of this month," he said.
However, the Pakistan Peoples Party (PPP) of exiled former Prime Minister Benazir Bhutto accused the government of rigging the elections and intimidation, after three of its activists were killed on Monday in a drive-by shooting near Attock.
The Human Rights Commission of Pakistan expressed some reservations although it said polling was largely peaceful and their teams did not notice any serious breach of procedures.
Opposition parties complain of
vote rigging in the by-elections
"The people witnessed a process that did not quite amount to a free and fair expression of the voters' will," it said in a statement. "There were many complaints of use of government resources and pressure in favour of the official candidate."
A major focus for Aziz's government is likely to be Pakistan's crackdown on al Qaeda and local Islamic militant groups, as the government seeks to sever ties between the military and Islamic radicals that go back decades.
Musharraf still wields ultimate authority, even after restoring parliament after elections two years ago. He retains the power to fire the prime minister and dissolve parliament.