The thermal Sunyaev-Zeldovich (SZ) effect and the X-ray emission offer separate and highly complementary probes of the thermodynamics of the intracluster medium. We presentJoXSZ, the first publicly available code designed to jointly fit SZ and X-ray data coming from various instruments to derive the thermodynamic profiles of galaxy clusters.JoXSZfollows a fully Bayesian forward-modelling approach, accounts for the SZ calibration uncertainty, and for the X-ray background level systematic. It improves upon most current and not publicly available analyses because it adopts the correct Poisson-Gauss expression for the joint likelihood, makes full use of the information contained in the observations, even in the case of missing values within the datasets, has a more inclusive error budget, and adopts a consistent temperature in the various parts of the code, allowing for differences between X-ray and SZ gas-mass weighted temperatures when required by the user.JoXSZaccounts for beam smearing and data analysis transfer function, accounts for the temperature and metallicity dependencies of the SZ and X-ray conversion factors, adopts flexible parametrisation for the thermodynamic profiles, and on user request, allows either adopting or relaxing the assumption of hydrostatic equilibrium (HE). When HE holds,JoXSZuses a physical (positive) prior on the radial derivative of the enclosed mass and derives the mass profile and overdensity radiirΔ. For these reasons,JoXSZgoes beyond simple SZ and electron density fits. We illustrate the use ofJoXSZby combining Chandra and NIKA data of the high-redshift cluster CL J1226.9+3332. The code is written in Python, it is fully documented, and the users are free to customise their analysis in accordance with their needs and requirements.JoXSZis publicly available on GitHub.