The decision by the 275-member body marks a political victory for Iraq’s Kurdish minority after suffering oppression under ousted dictator Saddam Hussein.
The announcement ends weeks of squabbling in the Iraqi parliament since the landmark January 30 elections.
Outgoing interim President Ghazi al-Yawar, a Sunni Arab, and Shi’ite Islamist Adel Abdel Mahdi, the finance minister in the outgoing government, were named as Mr Talabani’s deputies.
The presidential team will now select a prime minister, expected to be Shi’ite politician Ibrahim al-Jafaari.
Mr Talibani will be sworn in later on Wednesday.
The vote was a mere formality after the parliament formalised the line-up with Sunni parties on Tuesday.
The parliament selected its speaker on Sunday.
Saddam Hussein and 11 of his top aides are reportedly to watch the parliamentary proceedings from their jail cells in Baghdad, according to an AFP report.
“There will be a place in jail for Saddam and the 11 to watch the TV to understand they are no longer ruling the country; so they can understand in a new Iraq, people are elected and they are not coming to power by a coup d’etat,” said Human Rights Minister Bakhtiar Amin.
Shi’ite and Kurdish blocs in the parliament picked Mr Yawar for vice president late on Tuesday, filling a post reserved for Iraq’s fractured Sunni community.
“We are happy that the first elected president of Iraq is coming from a community that has been persecuted for years,” said Shi’ite MP Hussein Shahrastani.
Kurdish MP and outgoing foreign minister Hoshyar Zebari said his Kurdistan Alliance and the Shi’ite United Iraqi Alliance which dominated the elections have worked hard to reach out to embittered Sunnis.
Many Sunnis boycotted the election and they are seen as fuelling the country’s deadly insurgency.
The new parliament’s main task will now be to oversee the drafting of a permanent constitution, and to prepare for a second round of elections by December.