Analysts said Talabani, who speaks Farsi fluently after years of contacts with Iran when in opposition to Saddam Hussein, the Iraqi president, could press Iran to stop seeing Iraq as a battleground in its three-decade-old fight with Washington.
An Iranian official said Talabani would go straight into talks with Mahmoud Ahmadinejad, the Iranian president, and would leave on Tuesday after talks with Supreme Leader Ayatollah Ali Khamenei, Iran's highest authority.
"I think there has been some exaggeration about Damascus and Tehran's capabilities"
Mashaallah Shamsolvaezin, Iranian political analyst
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Asked last week what his talks in Tehran would cover, Talabani told Iranian state television: "Strengthening relations and Iraq's security."
He said then he would be accompanied by Iraq's oil, industry and technology ministers, and probably Hoshiyar Zebari, the foreign minister.
The visit is the latest of a series of contacts. Nuri al-Maliki, the Iraqi prime minister visited Tehran in September and secured a pledge of support for his government from Tehran.
Ahmadinejad said on Sunday Iran was ready to help the United States in Iraq, but only if it pledged to pull its troops out.
Iran had invited Bashar al-Assad, the Syrian president, to the talks, but Syria did not respond.
Iraq and Syria agreed last week to restore full diplomatic relations, in an accord in which Syria accepted that US troops should stay in Iraq while the Iraqi government needed them.
Syria has been accused of letting foreign fighters cross into Iraq. Iran is mainly accused of backing Shia militias and exporting arms, a charge Tehran dismisses.
An Iranian political analyst said Ahmadinejad's meeting with Talabani would in part aim "to show Iran has the influence and power to take the initiative before engagement [with the United States] starts".
Analysts said Iran had powerful friends in Iraq, but its influence had limits.
Mashaallah Shamsolvaezin, an Iranian political analyst, said: "I think there has been some exaggeration about Damascus and Tehran's capabilities."
The New York Times said on Monday a draft report prepared for an influential panel considering US alternatives for Iraq urged direct talks with Iran and Syria, but set no schedule for troop withdrawal.