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).
He is representing Yorro state constituency.
The tribunal had recently nullified the election that produced Mr Melaye as representative of the senatorial district at the upper legislative chamber and ordered that a fresh election be conducted.
The duo are yet to emerge officially as candidates of their party in the November 16 gubernatorial race.