Zardari indicated he would do away with these sweeping powers in 2009
The parliament of Pakistan has voted unanimously in favour of measures which limit key presidential powers.
The measures transfer certain powers from the office of the president to the prime minister and take away his power to dismiss elected governments.
Supporters say the legislation will strengthen parliamentary democracy, weakened by periods of military rule.
The bill was approved unanimously by Pakistan's National Assembly. It now needs approval from the upper house.
The constitution as it stands confers vast powers on the president, including the power to appoint military chiefs. That will end, as will the president's ability to dismiss all or any of the central or provincial governments in Pakistan.
Correspondents say the bill is likely to be approved by the upper house - or Senate - as all the major political parties have signed the draft. Once it is approved, it will pass into law.
"The impossible has been made possible by the house today," Pakistan's Prime Minister Yousuf Raza Gilani told lawmakers in a speech.
The BBC's Syed Shoaib Hasan in Islamabad says this is the first major constitutional amendment to empower parliament since 1973.
It is the first time since Pakistan became a nuclear power that the prime minister has been the most powerful person in the country - he now has his finger on the nuclear button.
Shoaib Hasan, BBC News, Islamabad
The constitutional amendment would empower the parliament and the prime minister- the elected representatives of the people.
It reduces the role of the president - a controversial one in recent times to that of a mere figurehead. The prime minister is now the most powerful man in the country - with complete control of Pakistan's nuclear and conventional forces.
The amendment also means that the appointment of judges - a thorny issue recently - no longer has executive oversight.
While the political elite have hailed these changes as historic, the public response has not been so complimentary.
Most people are of the opinion that the government should expend more energy in stabilising the inflation-ridden economy rather than passing what they say are "meaningless laws".
Under the new measures, the president becomes largely a figurehead who can dismiss parliament only on the advice of the prime minister, our correspondent says.
Other amendments include:
- The power to appoint judges being handed over to a judicial commission
- The president will no longer appoint the chief election commissioner
- Elections of the prime minister and provincial chief ministers will no longer be a secret ballot - an attempt to stop clandestine deals
- The president will no longer be able to impose emergency rule in a province unilaterally
President Zardari has been under lots of pressure to accept these measures, our correspondent says.
The amendment has been a long-standing policy of Pakistan's political parties, but especially of the Pakistan People's Party (PPP) - previously led by Benazir Bhutto, the murdered former prime minister and wife of Mr Zardari.
The changes to the constitution also rename North West Frontier Province as Khyber Pakhtoonkhwa - meaning "Khyber side of the land of the Pakhtuns".
The renaming of the province has been a long-standing demand of the ethnic Pashtuns who dominate the region.
In addition, the two-term limit on prime ministers is set to be lifted. This would allow opposition leader and two-time former Prime Minister Nawaz Sharif to try for another term.