The MEG experiment at the Paul Scherrer Institut (PSI) represents the state of the art in the search for the charged Lepton Flavour Violating (cLFV) μ⁺ → e⁺γ decay. With the phase 1, MEG set the new world best upper limit on the BR(μ⁺ → e⁺γ) < 4.2×10^-13 (90% C.L.). With the phase 2, MEG II, the experiment aims at reaching a sensitivity enhancement of about one order of magnitude compared to the previous MEG result. The new Cylindrical Drift CHamber (CDCH) is a key detector for MEG II. CDCH is a low-mass single volume detector with high granularity: 9 layers of 192 drift cells, few mm wide, defined by ~ 12000 wires in a stereo configuration for longitudinal hit localization. The filling gas mixture is Helium:Isobutane (90:10). The total radiation length is 1.5 × 10^-3 X₀, thus minimizing the Multiple Coulomb Scattering (MCS) contribution and allowing for a single-hit resolution < 120 μm and an angular and momentum resolutions of 6 mrad and 90 keV/c respectively. This article presents the CDCH commissioning activities at PSI after the wiring phase at INFN Lecce and the assembly phase at INFN Pisa. The endcaps preparation, HV tests and conditioning of the chamber are described, aiming at reaching the final stable working point. The integration into the MEG II experimental apparatus is described, in view of the first data taking with cosmic rays and μ⁺ beam during the 2018 and 2019 engineering runs. The first gas gain results are also shown. A full engineering run with all the upgraded detectors and the complete DAQ electronics is expected to start in 2020, followed by three years of physics data taking.