He said the president's decision was so closely-guarded no one saw it coming.
The Buhari-led federal government has also recognised the late Chief MKO Abiola as the winner of the annulled election.
According to Aregbesola, no one saw what Buhari did coming.
"Not even the snoopers in the corridors of power saw it coming. I don't know how many of you noticed the uncanny press release from President Buhari like a thief in the night. Presidents don't usually issue press statements. It was a masterstroke", Aregbesola said.
The Governor also said Buhari's apology to the MKO Abiola family was unprecedented.
Aregbesola also said the credit for the actualisation of the June 12 mandate should go to Asiwaju Bola Ahmed Tinubu.
"June 12 accentuated my relationship with Bola Tinubu. If anyone has to take credit for June 12, it has to be Bola Tinubu. Bola Tinubu told me that till his last breath, he will stand on June 12.
"When you have power, you get arrogant. Arrogance is synonymous with power. You must give it to Buhari for apologising for June 12. In the history of electoral processes in Nigeria, June 12 was the best. It takes a deep introspection to do what Buhari did", Aregbesola said.
Aregbesola also asked Buhari to formally recognise Abiola as a former president and have his photograph hung on the walls of Aso Rock as a former Nigerian president.