Mogaji died on June 15 at the age of 96.
The message, contained in a statement issued by Mr Emmanuel Yaweh, the Media Assistant to Babangida, said Mogaji left behind a legacy of excellence in service to humanity.
“I join you and all the family members in expressing gratitude to Almighty Allah for the life and times of the great lady.
“During her long eventful lifetime, she had recorded so many achievements that had touched on the lives of many Nigerians.
“She was a devout Muslim, a loving and caring wife, mother and grandmother, who showed affection to her family and all other people without discrimination.
“She dedicated her life to hard work and pursuit of excellence in the service of our people,’’ Babangida said.
He urged Tinubu to continue with the legacies of his late mother.
“Abibatu brought you up to be a well known, respected and admired leader, who is committed to defend the fundamental rights of all people.
“You are, therefore, roundly qualified to carry on her good deeds and works so as to keep alive the memory of her life.
“It is our expectation that you will undauntedly continue to forge and build on her legacy of honesty, dedication, trust, mobilisation, hard work, commitment and bridge building to enhance unity for the good of our country and people irrespective of creed or ethnicity.
“Your record of service to the good and great people of Lagos State and the rest of the federation and your political ideals, reach, structure and network are the evident fruits of her labour in nurturing, guiding and educating you so as to be useful to humanity,” Babangida said.