"An agreement has been reached by all the political parties," Khaled al-Attiya, an aide to Shia deputy parliament speaker, said on Sunday.
"They agreed to hold the first reading of the bill on federal regions on Tuesday, but will not be able to implement it until 18 months after parliament approves it."
The move came as Kurds began to debate their own constitution, a controversial document that sets conditions for the region to remain part of Iraq.
He also said a committee would be formed on Monday to start reviewing possible amendments to the constitution - a key demand of the Sunni minority.
"It will be formed and the day after the federalism bill will be read," Adnan al-Dulaimi, the Accordance Front leader, said.
Shia and Sunni politicians confirmed the deal but some said they still had reservations on the proposed draft that will be given to parliament on Tuesday.
Treating the problem
"We don't think this 18 month time-frame will do much to treat the problem, we need to agree on what the bill will say," said Hasan al-Shimmari, a spokesman for the small Shia party, Fadhila.
The committee will be made up of 12 representatives of the alliance, four from the Accordance Front, five Kurds, two members of Ayad Allawi's secular party, one member of Saleh al-Mutlaq's National Dialogue Front, one representative of the Yazidi minority religious sect, one Christian, and one Turkoman.
The committee will be headed by a member of the Sunni Accordance front.
The committee has four months to propose amendments, which then have to be approved by an absolute majority in parliament before being put to a referendum.
In a related development, Iraq's Kurdish parliament began debating the region's permanent constitution.
The 160-article document - a contentious proposal that lays claim to other parts of Iraq and sets conditions for the Kurds to remain part of the country - will be debated and amended in the run-up to a December 1 parliamentary vote by the Kurdish autonomous region's parliament.
According to Article Two, Iraq's Kurdish region consists of the three current provinces of Dohuk, Arbil and Sulaimaniyah, but also Kirkuk province and parts of Diyalah, Nineveh and Wasit provinces.
"The populations of these areas were taken from Kurdistan and when they are returned to Kurdistan, they will benefit from the same rights given to them by the federal constitution," stated the article.
The constitution goes on to state that the Kurds have "chosen a liberal federation with Iraq as long as it respects the federal constitution, its federal, democratic and multiparty parliament."