Talabani, 71, a Kurdish leader and head of the Patriotic Union of Kurdistan, took the oath on the Koran at a heavily-guarded ceremony in the Green Zone of central Baghdad.
Adel Abdel Mehdi, a Shiite, and Ghazi al-Yawer, the Sunni former transitional president, were sworn in as the president's deputies.
Jaafari now has two weeks to form the new government.
Earlier, Talabani said combating terrorism and drafting a new constitution with the consensus of all groups would be his priorities.
"We will seek to uproot terrorism and eliminate criminals while expanding democracy and freedom in all Iraq," Talabani told the mass-circulation Cairo daily, al-Ahram.
Talabani also said he wants to return Iraq to the Arab fold by reviving its role in the Arab League and improving Iraq's relations with all Arab countries without exception.
"We will also back the Palestinian people's right to set up their own independent state according to international resolutions and the Arab peace initiative," he said.