Spent catalysts generated from various processing industries such as those involved in the hydrogenation of fats and oils pose severe environmental issues if not treated and disposed of aptly. In this present work, process intensification was provided by the means of ultrasonic irradiation via an ultrasonic bath to ascertain the positive effects it imparts on the nitric acid and sulphuric acid leaching of spent silica-supported nickel hydrogenation catalysts. The extent of nickel recovered from ultrasound-assisted leaching was compared to that of the conventional mechanical stirring technique, whereby the actual ultrasonic densities of the ultrasound source were determined. Ultrasonic irradiation appreciably enhanced the extraction of nickel from the spent catalyst in all instances due to the physical and chemical effects of acoustic cavitation. In particular, sonication resulted in the expedited extraction of Ni, allowing a time reduction of 2 h in recovering ca. 70% Ni. Furthermore, it was also discovered that nitric acid was a more efficient leaching agent than sulphuric acid, achieving an improvement of ca. 20% in recovering Ni at 70 °C under ultrasonic conditions. Additionally, process optimisation was executed by adopting the response surface methodology, in which the modelled optimal conditions were ultrasonic bath amplitude = 67%, leaching temperature = 60 °C, nitric acid concentration 12.5 vol% and pulp density = 7.5%. Ultimately, the Ni recovery recorded under the optimal conditions was 99.37% in 2 h. Finally, an approximate economic analysis was performed to ascertain the recovery costs of nickel using the ultrasonic method. This study demonstrated the beneficial usage of ultrasound technology in the process intensification of hydrometallurgy, which could be employed on an industrial scale for higher recovery efficiencies and improved sustainability.