"We are satisfied. However, we have received a fax from the special court judge, in which, the judge, points that he will remain under the administrative control of the High Court," the bench said.
The apex court had in an order on July 19 this year, directed the extension of Justice Yadav's tenure until the trial is completed in six months, likely by April 30 next year.
The court had directed the Uttar Pradesh government to consult the Allahabad High Court to ensure that the tenure of the special judge is extended till the completion of the trial.
The development came after the judge wrote a letter to the top court in April this year seeking an extension of his tenure to complete the trial in the Babri Masjid demolition case.
Justice Yadav was set to retire on September 30, 2019.
In April 2017, the apex court had asked the special judge to complete the trial in two years.
Justice Yadav is hearing on a day-to-day basis, the case against senior BJP leaders -- Advani, Kalyan Singh and Murli Manohar Joshi -- in connection with the demolition of the disputed structure in Ayodhya on December 6, 1992.