"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.
He added that the assembly would meet on Monday to discuss the electoral law.
The draft was presented in parliament by Shaikh Humam Hammudi, the head of the constitution drafting panel after which a panel member began reading out its contents.
Munther al-Fadhal, a Kurdish-allied panellist said an overwhelming majority had signed the draft constitution.
"A few amendments have been done," he added.
Speaking in front of parliament, Hammudi, a Shia, congratulated the Iraqi people for "this constitution that was written by Iraqi hands".
However, two Sunni Arab negotiators said they would oppose the final text, insisting more should have been done to meet the minority's concerns.
"Surely we will reject the project (draft)," drafting committee
"We will reject the draft"
Sunni draft committee member
member Hassib Arif al-Obaidi said.
"We are in the middle of a meeting and will give our common
Fellow committee member Fakhr al-Qaisi also voiced opposition.
"We will reject the draft," he said, adding that an announcement to that effect would be made soon.
Iraqi negotiators have been racing against time to present a draft of the first post-Saddam Hussein constitution to the Iraq National Assembly after missing the first deadline on 15 August.
Iraqis will vote on the draft in a
referendum on 15 October
The draft now goes to the Iraqi people in a 15 October referendum. Five million copies will be circulated nationwide in food allotments each Iraqi family receives monthly from the government.
The amendments were made in the hope of appeasing the Sunni Arab minority, including removing the word "party" from the phrase about Saddam Hussein's Baath Party and allowing the parliament to be elected in December to decide the fate of a committee set up to purge former members.
But it was unclear if that was enough to appease the Sunni Arabs and whether the 15 Sunni negotiators signed the final document.
The parliament members of the committee appeared in the meeting hall for a group photo but made no statements.
The Sunni Arabs, who were appointed, did not attend. They are not parliament members.
Earlier on Sunday, Sunni negotiator Sadoun Zubaydi said "this is the end as far as the marginalised groups are concerned" and "as far as the drafting process is concerned".
"We now have to see how to proceed from here," he said.
The ceremony marking completion of the drafting process is set for 2.30pm (1430 GMT).
Al-Hassani (R): The draft will be
accepted despite Sunni objection
Shia legislator Mohammed Baqir al-Bahadli said "the constitution drafting committee has completed its work" and that an advertising and media campaign would begin right after the announcement to try to rally public support.
Earlier, Parliament Speaker Hajim al-Hassani had said the National Assembly would convene to accept the draft despite opposition from Sunni Arabs to portions of the document.
The interim constitution does not implicitly require legislative approval.