Zardari, co-chairman of the Pakistan Peoples Party (PPP), rose swiftly to power after the assassination of his wife, Benazir Bhutto at her own election rally last year.
He replaces Pervez Musharraf as chief executive after winning a parliamentary vote by a wide margin on Saturday.
Zardari's party heads a fragile coalition government which, although still in office, recently lost the backing of a key coalition party.
As president, Zardari will take charge of a country that has been riven by violence, with nearly 1,200 people killed in bombings and suicide attacks in the past year.
The economy is also in trouble, with rampant inflation and a plunging stock market that has lost around 40 per cent of its value since January.
Zardari is expected to outline his vision for Pakistan later on Tuesday, including his plans to counter the violence and turn around the economy, and whether he will continue Musharraf's policies of support for the US and its "war on terror".
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said: "The people of Pakistan are going to be watching to see whether Mr Zardari is going to support the American agenda, or the agenda that is acceptable to the people of Pakistan."