The tokamak cooling water system (TCWS) is the primary cooling system of the ITER tokamak machine, providing cooling water to the vacuum vessel and in-vacuum vessel components. In addition, it provides water and gas baking to its clients as well as drying them prior to maintenance activities. It is a Safety Important System that is subject to the French Order on Nuclear Pressure Equipment. The TCWS design has been modified significantly since the preliminary design. Such changes required the approval of the French Nuclear Safety Authority (ASN). The first main modification was to relocate the main equipment of the cooling loop for in-vessel components from level L4 to level L3 of the Tokamak Building in order to improve the overall building shielding capacities, and the second dealt with the ability of the TCWS to significantly reduce the mass and energy released in case of a loss-of-coolant accident (LOCA). This second improvement was required to allow a strong improvement of the vacuum vessel pressure suppression system (VVPSS), i.e., the system that prevents overpressure in the vacuum vessel in case of a LOCA. The green light for the two aforementioned modifications of the TCWS (together with the new VVPSS configuration) has been recently obtained from the ASN. Most recently, the three major subsystems of the TCWS needed for first plasma operations (to start the end of 2025) have passed the final design review process. The final design has been approved and procurement/manufacturing has started. In addition, the final design of all piping not functionally required for first plasma operation but nevertheless needed due to installation constraints has been reviewed and approved as well. A few kilometers of nuclear-grade piping have been delivered to the ITER Organization (IO) together with the main drain tanks of the system. All the other components are expected to be received on site starting May 2021. This paper gives a detailed description and status of the main TCWS subsystems needed for first plasma either because they are functionally required or because of installation constraints. The major modifications highlighted above as well as all the improvements accomplished in the final design are also detailed, together with a status on procurement and construction activities.