Early elections are expected in Israel following a Knesset vote today that starts the process of ending the current parliament.
Mr Sharon had earlier asked President Moshe Katsav to dissolve parliament, and then announced that he was leaving the Likud party.
The parliament decision means that will not now be necessary.
The Palestinian Deputy Prime Minister, Nabil Shaath, said Mr Sharon's resignation might speed up the resumption of the peace process.
Mr Sharon had written to the chairman of Likud, which he helped to found in 1973, informing him of his resignation and adding that he would form his own party.
Around 10 ministers and Knesset members were meeting him today to form a new centrist party, to be called National Responsibility.
The crisis followed yesterday's decision by the Labour Party, led by new leader Amir Peretz, to withdraw from the current coalition government.
77-year-old Mr Sharon has been battling hardliners within Likud who oppose giving up West Bank land.
EU ministers back border mission
Meanwhile, EU foreign ministers meeting in Brussels have given the go ahead to a new EU police mission which will oversee the Palestinian Authority assuming control of border crossings in Gaza.
The announcement follows agreement last week on allowing Palestinian control of the crossing into Egypt for the first time in many years.
The Minister for Foreign Affairs, Dermot Ahern, has said Ireland would pledge €200,000 towards the cost of the mission, which is the EU's first major involvement on the ground in the Middle East.
Last week, Israel agreed to let Palestinians control the border, but requested that a third party be involved to monitor the situation.
