Jammeh, who is accused of serious rights violations, led his country for 22 years but refused to accept defeat in a December election. He flew out of the capital Banjul late on Saturday as a regional military force was poised to remove him.
The peaceful end to the impasse will allow opposition figure Adama Barrow, who was sworn in as president at Gambia's embassy in neighbouring Senegal on Thursday, to take office.
Jammeh's decision to step down has prompted speculation over the terms agreed during two days of negotiations led by Guinea's President Alpha Conde and Mohamed Ould Abdel Aziz of Mauritania.
Regional leaders had not gone as far as agreeing immunity despite Jammeh's attempts to secure this, Senegalese Foreign Minister Mankeur Ndiaye told Reuters.
‘President Jammeh and his team concocted a declaration to be endorsed by (regional bloc) ECOWAS, the United Nations and the African Union that gave him every guarantee, essentially impunity,’ Mankeur Ndiaye said.
‘This declaration was signed by no one.’
The foreign minister made his comments after the AU and the UN published a joint declaration from the three bodies ‘with the purpose of reaching a peaceful resolution to the political situation in The Gambia.’
In it, they pledged, among other things, to protect Jammeh's rights ‘as a citizen, a party leader and a former Head of State’, to prevent the seizure of property belonging to him and his allies, and to ensure he can eventually return to Gambia.
However, Ndiaye played down the significance of the document.
‘I want to be clear on the fact that no ECOWAS head of state validated this declaration,’ said Ndiaye, who added that Barrow had not been made aware of the document before its publication.
TROOPS BEING DEPLOYED
Jammeh's loss in a Dec. 1 poll and his initial acceptance of the result were celebrated across the tiny nation by Gambians grown weary of his increasingly authoritarian rule. But he reversed his position a week later, creating a standoff with regional neighbours who demanded he step down.
Rights groups accuse him of jailing, torturing and killing his political opponents while acquiring a vast fortune - including luxury cars and an estate in the United States - as most of his people remained impoverished.
Jammeh flew to Equatorial-Guinea with a brief stopover in Guinea's capital Conakry, the office of Guinea's President Conde said on Sunday.
West African troops from Senegal, Nigeria, Ghana and Mali were deploying in Gambia on Sunday as part of efforts to secure the country and allow Barrow to take charge.
‘We will look for arms caches and detect mercenaries, so that we can restore calm,’ Marcel de Souza, president of the ECOWAS commission, told reporters overnight.
‘Adama Barrow hopes to go back as quickly as possible.’
A Reuters witness on Sunday saw war planes flying over the capital Banjul, which remained calm despite some concern over how the army, a pillar of Jammeh's regime, would react to his departure.