Osinbajo was spotted at the Abuja House, the Nigerian High Commission in London, by a Reuters reporter late in the evening.
He did not comment as he entered the building, where he spent one hour with the President.
As he exited the Abuja House, the Acting President also did not answer questions or give any comments on what was discussed.
His media aide, Laolu Akande, had confirmed that Osinbajo would be in London to see Buhari, who has spent the last months on medical leave.