Tinubu was said to have released his private jet on the condition that Jammeh exits Gambia immediately.
According to The Nation, there was no plane to fly Jammeh out of Gambia after he finally agreed to leave office on Saturday night - this followed last-minute pressure from Guinean President Alpha Conde and his Mauritanian counterpart Mohammed Ould Abdel Azizthere.
It was reported that the leaders then contacted Tinubu, who authorised his private plane - VP-CBT Falcon Jet - to be used to fly Jammeh out of Banjul, Gambia's capital.
The All Progressives Congress leader was said to have given the condition that the plane should only be used "if it will facilitate the quick exit of Jammeh and lead to the restoration of peace and democracy in The Gambia."
Consequently, the plane flew out Jammeh, his wife, mother and Conde to Equitorial Guinea.
It was gathered that, before their departure, Senegal insisted on knowing those on board before allowing the plane to overfly its airspace - the demand was granted.
Jammeh's exit marked the end of 22 years of dictatorship in the tiny West African country.
He had rejected the results of the December 1 presidential election, which was won by Adama Barrow.
For weeks, ECOWAS leaders had persuaded him to step down but he refused until an army was raised by the African Council, with troops drawn from Nigeria, Senegal, and Ghana to remove him by force.
He was said to have surrendered and agreed to go on exile in Guinea on Saturday night.