Speaking shortly after he met the the rescued girls on Thursday, Osinbajo said:
"There was no swap of any kind. Even when we started negotiations, we said we will consider all options available to us. Absolutely, there was no exchange of any kind this time.
"But we must be sensitive to the fact that the government wants these girls back and alive, again, we must balance it against the security and safety of the country,.
"I also want to thank the military and all the security services, DSS, intelligence services across the county as well as our friends and partners, internationally who have also helped in bringing happy ending of captivity of at least 21 of the Chibok girls.
"About an hour ago, I met with the 21 Chibok girls who have been brought back and they are in good health, considering the circumstances they have been held in and they are now being well taken care of in the medical facility.
"In the process of negotiation, we will look at all options and we will weigh the options carefully and decide what to do.
"But what has happened and the process we have begun is one which has not involved any type of swap of Boko Haram commanders or any militant in any way.
"It is a very good turn of event. We believe that in the next few days and months, we will be bringing in more of these girls using exactly the same kind of negotiation and the same template that we used.
"They will be staying at the hospital for some time until we are satisfied about their health condition. Their parents will be coming to join them hopefully by tomorrow, Friday.
"There will be therapy, there will be counselling. Of course, we can imagine what they must have gone through. So we expect that a lot of psychological therapy and so much need to be done to get them back.
"The Swiss government worked with us in the process of negotiation but the Red Cross is not involved in the negotiation but in taking the girls back, of course, we worked with the Red Cross because we were unable to take our own medical team there.
"The Red Cross was not involved at all in the process of negotiation. It was the Swiss government, our own officials: the DSS, intelligence and the military were the ones involved.
"One of the 21 girls has a baby. She is the only one."