The Acting President's meeting with President Buhari in London reportedly lasted for an hour.
The meeting, their first since May 7, took place at the Abuja House where the president has been recovering from an undisclosed illness.
There are no pictures of the meeting, which reportedly lasted for an hour, but a video has emerged of the Acting President leaving the Abuja House after the meeting.
Osinbajo's spokesperson, Laolu Akande, tweeting with his Twitter handle (@akandeoj), had previously said the Acting President would return immediately after the meeting.
He tweeted, "AgP Osinbajo meeting with President Buhari in London today, and returning to Abuja immediately afterwards."
This morning, he confirmed that Osinbajo was back in Abuja, the country's capital, tweeting, "AgP Osinbajo now back in Abuja from London & will be presiding over FEC this morning starting @ 11am at the Council Chambers in Aso Rock".
He had also earlier promised that details about the meeting would be shared with the Nigerian people later when he tweeted, "We will soon share more information about AgP Osinbajo's London meeting with President Buhari. It was a very good meeting. God bless Nigeria".
President Buhari has been in London since he left Nigeria on May 7 to resume treatment for an undisclosed ailment he had first treated on his earlier trip this year.
His wife, Aisha, had also visited him for the second time on Wednesday, July 5, returning to the country this week.
She had first visited him on May 30, before returning on June 6 to assure Nigerians that the president was getting better.
She said, "My husband is recovering very fast. And very soon, he will return to the country to resume his official duties."