During the visit, Tinubu told Nigerians he would not disappoint them.
Mr Tinubu, according to a statement from his media office made available to journalists said he arrived to a tumultuous welcome at the presidential wing of the Murtala Muhammed Airport, Ikeja.
The statement signed by Tunde Rahman noted that the president-elect was received among others by the Lagos State Governor Babajide Sanwo-Olu, Chief of Staff Tayo Ayinde, Musiliu Obanikoro and other top functionaries in Lagos.
The train then proceeded to the Iga-Iduganran Palace where the Oba of Lagos, Rilwanu Akiolu, some other traditional rulers in the state and White Cap chiefs were already waiting.
Addressing the modest crowd gathered inside the palace, Mr Tinubu, a former governor of the state, likened the primaries and election he went through to a World Cup tournament while thanking God and the people for his eventual victory.
Tinubu at the palace.
He said his message was one of gratitude, adding, however, that he would work assiduously for Nigeria from the get-go and would not disappoint the people.
Speaking in Yoruba, he specifically thanked Oba Akiolu and other traditional rulers in the state for their prayers and support.
Mr Akiolu described the president-elect as a special breed “who is destined for leadership at the very top.”
Other traditional rulers gathered at the palace included Elegushi of Ikate-Elegushi Kingdom, Oba Saheed Elegushi, and Oniru of Iruland, Oba Omogbolahan Lawal.
Also at the palace were former Deputy Governor Femi Pedro, former Commissioner for Environment in Lagos, Muiz Banire, and the All Progressives Congress Woman Leader in the state, Hon. Jumoke Okoya-Thomas.