He quit unexpectedly two weeks ago during a visit to Riyadh, but his resignation has not been accepted.
Mr Hariri denied widespread allegations that he was held in Saudi Arabia against his will, tweeting that the claims were "a lie".
Lebanon's president said on Saturday that Mr Hariri had told him he would be back in the country by Wednesday.
President Michel Aoun said on Twitter that Mr Hariri had told him by telephone that he would return for independence day celebrations.
Mr Hariri is expected to meet French President Emmanuel Macron on Saturday morning and then visit a number of Arab capitals.
Meanwhile, Saudi Arabia has recalled its envoy to Berlin over comments by Germany's foreign minister suggesting Mr Hariri was held against his will.
"Saudi Arabia has decided to recall its ambassador to Germany for consultations and will give the German ambassador in the kingdom a letter protesting these unfortunate and unjustified statements," the Saudi state news agency SPA said.
"Mr Hariri left Riyadh airport on his private jet with his wife and is headed for Le Bourget airport (near Paris)," Future TV announced early on Saturday.
On Wednesday, President Macron said he had invited Mr Hariri and his family to Paris after the French leader spoke by telephone to Saudi Crown Prince Mohammed bin Salman.
The French president was later forced to clarify that he was not offering political exile, and that he expected Mr Hariri to stay only "for a few days".
France, Lebanon's former colonial ruler, has been trying to mediate in the crisis.
Mr Hariri's departure for France marks a new chapter in an extraordinary political crisis which continues to be a source of intense speculation as well as condemnation, the BBC's Lyse Doucet says.
Lebanese officials had earlier said Mr Hariri was being detained in Saudi Arabia - a claim denied as "false" by Riyadh.
Saudi Arabia has also denied forcing Mr Hariri to resign in an attempt to curb the influence of its regional rival Iran and its Lebanese proxy Hezbollah, which is part of a national unity government that Mr Hariri formed last year.
Mr Hariri announced his resignation in a televised address from Riyadh, in which he accused Iran of sowing "discord, devastation and destruction" in the region and said he sensed there was an assassination plot against him.
His father Rafik - himself a former Lebanese prime minister - was killed in a car bombing in Beirut in 2005.
Several members of Hezbollah are being tried in absentia at a UN-backed tribunal at The Hague in connection with the attack, though the group has denied any involvement.
Mr Hariri has close ties with Saudi Arabia. He holds both Lebanese and Saudi citizenship, owns properties in the kingdom, and Riyadh is a key backer of his political party, the Future Movement.
No comments: