The apex court sitting in Abuja gave the verdict in its ruling on Monday morning.
Electoral violence, ballot box snatching, vote buying among others marred the exercise which began on Saturday.
Meanwhile, Melaye has rejected the result of the election, calling for its cancellation.
The both parties are projected to retain power in their domain.
The lawmakers were said to have arrived the venue late and were prevented from entering the government house on the orders of the state governor.
The ruling is in favour of his opponent, Smart Adeyemi, who won at both the tribunal and the appellate court.
The oath of office was administered to the new deputy governor by Justice Nasiru Ajanah, the Chief Judge of the State.
Meanwhile, Achuba is reported to have proclaimed himself as the authentic deputy governor of the state.
The request is coming a month to the scheduled date for the governorship election wherein the state governor, Yahaya Bello, is seeking another term in office.
The election of the opposition lawmaker is been challenged by Smart Adeyemi of the ruling All Progressive Congress (APC).