"The draft constitution is ready and will be presented to the Iraqi people, who are known for their intelligence, to give their verdict on October 15," Talabani told reporters at a ceremony to mark the end of the drafting process.
"There are objections from our Sunni Arab brothers ... but nobody can claim that they represent the whole spectrum of Sunni Arabs," said the president, who is a Kurd. "If the nation rejects it, we will write another one."
After the final draft was formally presented to parliament, US ambassador Zalmay Khalilzad called the charter "the most progressive document of the Muslim world".
He said it reunited Kurdish northern Iraq with the rest of the country.
"The Kurdish leaders are bringing their region back into Iraq," he said, noting Iraqi Kurdistan had been running its own affairs since the country's defeat in the 1991 Gulf War over Kuwait.
He also said the charter protected women's rights.
"Iraqis from all communities should review the draft ... because there have been misinterpretations ... and they should decide for themselves on how to vote," Khalilzad urged.
Negotiators agreed 11th-hour changes to the text in a bid to win endorsement from the alienated former Sunni Arab elite whose community has driven the anti-US insurgency.
But the changes appeared to have failed to bring the Sunnis on board.
"The constitution is a gift to the Iraqi people," deputy parliament speaker Hussein al-Shahristani said after the entire text of the charter was read out in front of lawmakers in the Shia- and Kurdish-dominated chamber.
The text was signed by Iraq's three-man presidency, which includes Sunni former president Sheikh Ghazi al-Yawar. The parliament session ended without any vote on the text.
The ceremony ended weeks of talks to thrash out the text but paves the way toward the potentially even more awkward obstacle of the October 15 referendum on the draft that could see the process go back to square one.
Shia negotiator Khudair al-Khozai acknowledged that just three of the 15 Sunni Arab members had turned up for the final meeting of the drafting committee.
He said the 11th-hour concessions made to the Sunnis had been "minor and do not affect the core" of the text.
The principal stumbling block throughout the protracted talks had been Shiite demands for an autonomous region in Shia-majority areas of the centre and south like that of the Kurds in the north.
Sunnis consistently opposed the demand amid fears they would lose out in the distribution of Iraq's huge oil revenues under a fully federal system, given that the reserves lie almost entirely in the Kurdish north or Shia south.
The final draft said the political system of Iraq would be "republican, parliamentary, democratic and federal", and referred to Islam as "a main source of legislation".
It also did not meet Sunni demands to describe Iraq as being part of the Arab world, sticking to the earlier version, which said, "Arab people in it (Iraq) are part of the Arab nation."
Shia negotiators said they had moderated their position on an autonomous region, insisting only on the principle of federalism and leaving it to a new parliament to work out the details after elections due by mid-December.
Sunni delegates said they continued to oppose the text but would not abandon the political process ahead of the elections.
"There are disputed points which cannot be overlooked because they lead to the dismantling of the country," they said in a joint statement.
"We decided to reject these points ... but this would not stop us from... taking part in the political process to reach a unified Iraq, starting with the elections."