© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.In gauge invariant theories, like Einstein-Maxwell theory, physical observables should be gauge invariant. In particular, mass, entropy, angular momentum, electric charge, and their respective chemical potentials, temperature, horizon angular velocity, and electric potential, which appear in the laws of black hole thermodynamics, should be gauge invariant. In the usual construction of the laws of black hole thermodynamics, gauge invariance of the intensive quantities is subtle; here, we remedy this and provide a gauge invariant derivation and the proof of the zeroth and first laws of black hole thermodynamics.