It was not immediately clear whether the Palestinian parliament would be dissolved as a result of Mr Arafat's decree.
But a potentially damaging vote of no confidence in Mr Arafat's cabinet - scheduled to take place within hours - will now be void.
A significant number of deputies had been expected to vote against Mr Arafat's new line-up - appointed under international pressure in June - at the parliamentary meeting in Ramallah.
Rawfi Fatukh, secretary general of the Palestinian parliament, said: "Arafat is to issue a decree on the election date, meaning automatically that the cabinet is a caretaker government which does not need a confidence vote."
Mr Arafat's election decree read: "The Palestinian people in the Gaza Strip, the West Bank and Jerusalem are invited to free and direct general elections, to elect the head of the Palestinian National Authority and members of the Legislative Council on Monday, 20 January, 2003."
US President George W Bush has urged the Palestinian people to drop Yasser Arafat and bring in new leaders uncompromised by "terrorism".
Palestinians last held elections in 1996.
A BBC correspondent in Jerusalem, Peter Biles, said it was hard to see how there could be open democratic elections in just four months, given the military restrictions still imposed on Palestinians.
But our correspondent suggested that the announcement of a date for the election could be used to try to push Israel to allow more freedom in Palestinian areas leading up to the vote.
Renewed support
Mr Arafat has now won support for his controversial cabinet from deputies of his Fatah movement whom he met on the fringes of the meeting of the Palestinian Legislative Council.
There had been opposition to his cabinet changes, with some deputies wanting more changes.
There are also divisions in Fatah over an announcement that it is rejecting attacks on Israeli civilian targets and will try to prevent them.
Officials from Fatah said there was backing for the move from its own military wing, Tanzim, and said they would ask militant groups such as Hamas to do the same.
Mr Arafat himself condemned all attacks against Israeli civilians in a speech to the Palestinian parliament which is continuing to meet at Mr Arafat's headquarters in Ramallah, still surrounded by the Israeli Army.