The Gran Telescopio de Canarias Adaptive Optics System (GTCAO) is currently in its commissioning phase at Roque de Los Muchachos Observatory (ORM). The GTCAO is a single-conjugated post-focal system equipped with a Shack- Hartmann Wavefront Sensor (WFS) and a Deformable Mirror (DM) conjugated to the pupil, achieving a Strehl Ratio of 65% in the K-band by utilizing a natural bright star. By early 2023, the development of the AO system concluded at the facilities of the Instituto de Astrofísica de Canarias (IAC), where acceptance tests were carried out. Subsequently, the entire system was integrated onto the Nasmyth platform of the telescope, replicating the controlled laboratory conditions. During maritime and land transportation, the system was handled with the optics train integrated and high-precision alignment. This involved the development of specific transportation tools to prevent accelerations beyond 2g, which could induce plastic deformations and misalignments in the opto-mechanical components. Extensive vibration analysis and different Power Spectral Densities (PSD) profiles were crucial to meet the requirements. A rigorous integration procedure was devised to ensure safe assembly, spanning four consecutive daytime shifts. This meticulous approach was adopted to guarantee that the telescope's observing hours remained uncompromised. This article provides a comprehensive account of the integration process and emphasizes the mechanical aspects. It includes static and dynamic mechanical analyses and technical details of handling, transport, and integration from the lab to the telescope to ensure safety and high precision assembly of opto-mechanical components.