Obasanjo said Akunyili, who died from cancer in 2014, was a woman of virtue, character and integrity.
Obasanjo, during his administration, had appointed Akunyili to head the National Agency For Food Drug Administration And Control (NAFDAC).
Speaking at the 14th annual lecture of the Women in Management Business and Public service in Lagos, the Obasanjo explained why he chose Akunyili for the job.
He said, "I was looking for somebody who would work in NAFDAC.
"There was an old man who was there and didn’t really impress me. I had had a couple of meetings with him and I found him not (to be) the type of man I would want to have on that job.
"I was talking to a friend who said, ‘Oh, there is a lady; she went to Britain for a medical (program) and when she finished, she said whatever money was left from the money deposited by her department should be sent back to the department.
"And the people called her and said, 'Are you not a Nigerian? Nigerians will come here and say add something which you would pay back to us later.'
"So, I said there is a Nigerian woman like that, where is she? .
"So, I located Dora and I said, ‘What is your profession?’ She said, pharmacy. I said pharmacy; I am looking for a pharmacist for this job. She got the job."
The former President also encouraged women to get actively involved in politics.
Akunyili served as NAFDAC director-general and Minister of Information and Communications from 2008 to 2010.
She ran for election as senator for Anambra Central in April 2011 under the platform of All Progressives Grand Alliance (APGA) but she lost to Chris Ngige of the Action Congress of Nigeria (ACN).
After a long battle with cancer, Akunyili died in an Indian hospital on June 7, 2014.