Lawmakers chose interim President Ghazi Ajil al-Yawir, a Sunni Arab, along with Shi'ite candidate Adel Abd al-Mahdi to be Iraq's two vice presidents.
Talabani said before parliament that he hopes to unify the country and will "spare no effort to present Iraq as a model of democracy."
Today's vote came after about nine weeks of political deadlock on forming a coalition government. The legislature that chose him emerged from national elections on 30 January.
Iraqi political leaders expect Islamist Shiite politican Ibrahim al-Jaafari to be named prime minister on Thursday. Deputy speaker Hussein al-Shahristani said the three leaders are to be sworn in as early as Thursday.
Talabani's selection comes almost two years after former President Saddam Hussein was ousted by a U.S.-led invasion force.
Talabani is secretary-general of the Patriotic Union of Kurdistan (PUK)
party. He told the inaugural session of the Iraqi National Assembly on 16 March that the country faces a difficult challenge uniting all Iraqis.
"A serious patriotic task stands before all of us: It is reestablishing the previous Iraqi national unity on the principles of free choice, consensus, and national reconciliation between Iraqis of goodwill who are against dictatorship and terror," Talabani told lawmakers.
(Reuters/AP/AFP)[For more on events in Iraq, see RFE/RL's dedicated webpage.]