Mrima said public interest demanded that the office of the deputy president not remain vacant.
He said the three-judge bench had chosen to abide by the calling that everyone has the obligation to respect, uphold and respect the Constitution.
"We are convinced and find that the current constitutional framework does not envision any scenario in which the office of the Deputy President would remain vacant except during the brief period required to fill a vacancy," Justice Anthony Mrima said.
The three-judge bench is led by Justice Eric Ogola and is comprised of Mrima and Justice Fredah Mugambi.
David Munyi Mathenge and Peter Gichobi Kamotho sought the orders after the National Assembly approved the nomination of Kindiki as the new Deputy President, a day after the Senate voted to impeach Rigathi Gachagua.
Mathenge and Kamotho have sued the Senate, the Speaker of the Senate, and two others.
The case was filed under a certificate of urgency before Justice Mwongo Richard Mururu. The case was later consolidated with others that had been filed in Nairobi.
While addressing the court, the National Assembly led by former Attorney General Githu Muigai argued that the office of the deputy president was vacant and that the conservatory order had been overtaken by events.
On October 11, the High Courts in Nairobi and Kerugoya issued conservatory orders stopping the appointment and swearing-in of Kithure Kindiki as the deputy President.
"The applications for conservatory orders are hereby disallowed. The conservatory orders on October 18, 2024, in Kerugoya High Court are hereby discharged and set aside," Justice Eric Ogolla pronounced.