•A large custom cryogen-free cryostat has been designed and built in order to operate the CUORE detector.•The CUORE cryostat has a 1 m3 experimental volume and is able to host a tonne-scale bolometric detector.•The CUORE cryostat guarantees a low noise and low radioactivity environment, needed to search for 0nbb.•The CUORE detector has been cooled down to 8.3 mK and steadily operated at 15 mK, proving the success of the cryostat.