The APC was represented at the tribunal by Yomi Ariyo, a Senior Advocate of Nigeria, who led six other counsel.
Justice Suleiman Belgore, while granting the prayers, gave reasons for granting the application which was filed on July 31.
He said the counsel had sought the order of the court to access the election materials in order to make photocopy of the documents of the election materials and to use forensic equipment to view the handwriting of the election result and the fingerprint of the election materials.
The request, he also said, was to obtain and photocopy all the election materials which were also in custody of the first respondent, the Peoples Democratic Party (PDP).
He added that the request was to seek forensic experts to access both machine and other materials used in the conduct of the election.
The tribunal chairman granted the application, saying this was also approved for the PDP.
The News Agency of Nigeria reports that APC candidate, Dr Kayode Fayemi, was declared the winner of the election by the Chief Returning Officer, Prof. Idowu Olayinka, after securing 197,459 votes.
The PDP candidate and current Deputy Governor, Prof. Kolapo Olusola, scored 178,121 votes.