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 charge $e$, Kerr-like rotation $a$, and the value of the external 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 [Phys. Rev. Lett. {}, 181401 (2025)] has a special charge, and we identify a genuine uncharged Kerr black hole immersed in the magnetic field. In the weak-field limit, it gives the Wald solution. We analyze the main physical properties of the new family, namely singularities, horizons, regularity of axes, charges, entropy, and temperature.