He said that Obasanjo had no moral justification to ask President Muhammadu Buhari not to re-contest the Presidency in 2019.
Tinubu said this at the National Convention of APC in Abuja.
He went on to describe Obasanjo as a “busy body”, arguing that the achievements of President Buhari in three years could not be compared to those of the administrations of the Peoples Democratic Party (PDP) that ruled the country for 16 unbroken years.
He also added that the ex-President, Obasanjo is not a member of the APC nor any other political party having torn his Peoples Democratic Party (PDP) membership card publicly.
Mr Obasanjo was President between 1999 and 2007 on the platform of the PDP.
The former President had earlier in the year written an open letter to Mr Buhari asking him not to run for a second term because he had performed poorly.
However, the president ignored the advice as he announced at the APC National Executive Committee (NEC) meeting in Abuja that he would seek reelection next year.
Mr Tinubu, a former governor of Lagos State, said Mr Obasanjo did not have the right to tell the president not to run again.
He added that he was happy to be in the APC and not listening to those who advised him against associating with President Buhari.
He thanked Buhari for his tenacity and commitment to fight corruption in the country and for working hard to develop the country.
He also appreciated Vice President Yemi Osinbajo for being “a great fountain of knowledge” and for not undermining his (Vice President) leaders.