Osinbajo stated this at a dinner organised in honour of President Muhammadu Buhari and himself at the State House Banquet Hall.
Buhari and Osinbajo had earlier in the day been sworn-in for a second term in office by the acting Chief Justice of Nigeria, Justice Tanko Muhammad.
The president, who is billed to depart for Makkah, Saudi Arabia on May 30 for OIC summit, was represented at the dinner by the vice president.
“Something interesting happened earlier today; I am a lawyer and a law teacher and I like to test and interrogate legal scenarios.
“At one minute past midnight today, the four year term of the President and I ended by effluxion of time.
“So, from one minute past 12 of last night, May 29 to about 10:30 am when we were sworn in for a second term there was no President or Vice President.
“Interestingly nothing went wrong, all was okay; when such a situation arises, it is the Senate President who acts as President.
“So, when I arrived at Eagle Square this morning, some may have noticed that the Senate President and I were enjoying a joke.
“He said to me jokingly `you better be careful you know I am the acting President now’; so, we thank the Senate President for not doing anything funny.’’
The vice president said that the beauty of democracy was the orderly and civilised process of transition and more importantly, the sanctity of and respect for the will and choice of the people.
He said that on Feb. 23, the Nigerian people freely made a choice to re-elect Buhari for a second term in office.
Osinbajo said it was a choice that was celebrated with pomp and pageantry earlier in the day.
He expressed gratitude to God and Nigerians for trusting the administration yet again as that trust would not be betrayed.
“And so on behalf of the President, please accept our deepest gratitude for your support and presence here this evening.
“The best years of Nigeria begin today, and by the Grace of God all of us will live to enjoy the coming years and many more,’’ he said.
In his address, Mr Boss Mustapha, Secretary to the Government of the Federation (SGF), said the inauguration was the official commencement of a new mandate given to the President by Nigerians.
He said that the new mandate was a reflection of the confidence Nigerians had in the administration.
Mustapha said the inauguration marked the beginning of the journey to the Next Level and consolidate on the foundation laid in the last four years.
He solicited the support of every Nigerian including the opposition for the administration in moving Nigeria forward.
In a toast, the All Progressives Congress (APC) National Chairman, Adams Oshiomhole, said that Nigeria had a peaceful and successful general election.
He said it was only in peaceful environment that sustainable development could be achieved.
Oshiomhole said the celebration was for all Nigerians not just for APC.
The dinner attracted former Head of State, Yakubu Gowon, service chiefs, Head of Civil Service of the Federation, members of the National Assembly, APC chieftains, members of the diplomatic corps and captains of industry. (NAN)