"Talabani arrived in Tehran minutes ago as the head of a high-level delegation," Iran's state-run television reported.
Talabani had planned to come to Tehran on Saturday but had to postpone his trip until Baghdad's airport, which was closed in a security clampdown, reopened Monday.
Iranian officials have said an invitation was extended to Assad, but Syria has not responded.
Talabani was given a red-carpet welcome by Ahmadinejad at Iran's Presidential Palace and the two presidents were expected to begin talks later Monday, the television reported.
The Iraqi leader also is scheduled to meet Iran's former president, Hashemi Rafsanjani, later Monday and Iran's top leader, Ayatollah Ali Khamenei, on Tuesday.
The United States has refused to negotiate with Iran and Syria to seek their support to bring stability to Iraq, accusing both Tehran and Damascus of aiding insurgent groups in Iraq.
Iran is believed to back Iraqi Shiite militias blamed in sectarian killings that have killed thousands this year. Iran has repeatedly denied the allegations.
But U.S. President George W. Bush, who was scheduled to meet with Iraq's Prime Minister Nouri al-Maliki later this week in Jordan, has come under increasing pressure at home to engage Iran and Syria into a dialogue.
The New York Times reported in Monday's editions that a draft report by the study panel led by former U.S. Secretary of State James A. Baker III recommends increased regional diplomacy, including holding talks with Iran and Syria.
Ahmadinejad has said Iran is willing to help Washington with Iraq if the U.S. drops its "bullying" policy toward Tehran. Iran also has made clear that it wants to exert its influence in Iraq on Tehran's terms, not Washington's.
"(Iraq's) occupiers need countries to help them get out of the quagmire," IRNA quoted Foreign Minister Manouchehr Mottaki as saying Monday.
Syrian officials have been silent for days over whether Assad would attend, apparently to avoid embarrassing Iran with a direct rejection.
Iran is Syria's only close ally and a rejection would be an unusual snub, but Damascus may be more worried about angering the United States by joining Iran's overt attempt to assert itself in Iraq. Instead, Syria may likely be looking further down the road to potential talks with Washington.
It is the fourth visit by Talabani, who speaks fluent Farsi, since he took office. He is a member of Iraq's Kurdish minority, but he had close ties with Iranian officials before Saddam Hussein was driven out by the U.S.-led invasion in 2003.