We present a spacetime that describes a rotating and charged black hole immersed in an external magnetic (or electric) field which is oriented along the rotational axis. This solution is characterized by four physical parameters, namely, the black hole mass $m$, its electric charge $e$, Kerr-like rotation $a$, and the value of the external magnetic field $B$. Such exact solution to the Einstein-Maxwell equations has a surprisingly simple form. Moreover, for $B=0$ it reduces to standard Kerr-Newman metric, while for $m=0$ and $e=0$ we recover the Bertotti-Robinson universe with a uniform (electro)magnetic field. We also show that the Kerr-BR solution presented in Podolský and Ovcharenko [Kerr black hole in a uniform Bertotti-Robinson magnetic field: An exact solution, Phys. Rev. Lett. 135, 181401 (2025).] has a special charge, and, contrary to it, we identify a genuine uncharged Kerr black hole immersed in the magnetic field. In the weak-field limit, this spacetime gives the Wald solution. We analyze the main physical properties of the new family, namely, singularities, horizons, regularity of axes, charges, entropy, and temperature.

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• Classical black holes
• Classical solutions in field theory
• General relativity
• Gravitation
• Differential equations
• Geometry