The constitutional change, which has been sought by Erdogan since he became president in 2014, would see Turkey switch to an executive presidency along the lines of the United States or France.
But it has become the latest polarising issue surrounding the Turkish strongman, who has been accused by opponents of increasingly authoritarian rule especially after the attempted coup in July.
The drive for the change comes at a critical time for Erdogan, with the relentless crackdown after the coup straining ties with the West and the Turkish lira under severe pressure.
The announcement followed months of talks between the ruling Justice and Development Party (AKP) led by Yildirim and the Nationalist Movement Party (MHP).
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The MHP is the fourth largest party in parliament but the AKP needs its support for the 330 votes required to call a referendum on the issue.
Yildirim said the bill would "save our country" from coups after Erdogan saw off a putsch aimed at ousting him from power on July 15.
Turkey had on three previous occasions since 1960 seen governments directly ousted by the military, which considers itself the guardian of secular Turkey.
The AKP has only 316 seats (excluding the speaker of the parliament) and needs at least 14 votes from the MHP to secure a three-fifths majority required to call the referendum.
Deputy Prime Minister Nurettin Canikli told broadcaster A Haber that "consensus had been secured" between the MHP and AKP and a referendum could take place in March, April or May.
The main opposition Republican People's Party (CHP) and the pro-Kurdish Peoples' Democratic Party (HDP) vehemently oppose changing the parliamentary system.
CHP leader Kemal Kilicdaroglu said the changes risked wrecking the parliamentary system that goes back to reforms in the late Ottoman Empire.
"This is a regime change, not a system change," he told NTV television.
"This country has a 140-year parliamentary system tradition. There are disruptive directions here and they can be corrected.