Mr Jammeh travelled to the airport in The Gambia’s capital Banjul with mediator Alpha Conde, the president of Guinea, as he headed into exile.
As he climbed the stairs to the plane, Mr Jammeh kissed his copy of the Koran, and waved to supporters before going inside.
Sky News Chief Correspondent Stuart Ramsay said: “It’s an end of quite an era, an end of a very difficult month for the country where they thought they were about to get invaded.
“It was made quite clear to him that he had to go, and he knew time was up when his own military said they would not fight to defend him.”
Mr Jammeh had refused to step down after he lost an election to President Adama Barrow, but bowed to pressure from the West African military that had entered The Gambia to force him to recognise the election outcome.
Speaking earlier on Saturday, he told state television: “I have decided today in good conscience to relinquish the mantle of leadership of this great nation.”
Mr Barrow was inaugurated on Thursday in neighbouring Senegal, with support from the international community.
He said on Saturday he would return to Gambia once it is “clear” and a security sweep is completed.
Mr Jammeh’s departure ended hours of last-minute negotiations with the leaders of Guinea and Mauritania.
Human rights activists have demanded he is held accountable for alleged abuses – including the torture and detention of opponents.
It was concerns about prosecution that led to him challenging the election in December, days after he had initially conceded defeat.
Jeggan Bahoum, of the Movement for the Restoration of Democracy in Gambia, said: “Jammeh came as a pauper bearing guns. He should leave as a disrobed despot.
“The properties he seeks to protect belong to Gambians and Gambia, and he must not be allowed to take them with him.”
An online petition also called for him to be denied asylum and instead arrested.
Mr Jammeh seized power in 1994 in a coup, and had been holed up in his official residence in Banjul as he was abandoned by his security forces.