Nonperturbative treatment of the quark-hadron transition at nonzero temperature $T$ and chemical potential $\mu$ in the framework of the field correlator method is generalized to the case of nonzero magnetic field B. A compact form of the quark pressure for arbitrary $B,\mu ,T$ is derived. As a result, the transition temperature is found as a function of B and $\mu$, which depends only on the following parameters: the vacuum gluonic condensate $G_2$ and the field correlator $D_1^E(x)$, which defines the Polyakov loops and is known both analytically and on the lattice. A moderate (25%) decrease of $T_c(\mu =0)$ for $eB$ changing from zero to $1{\mathrm{GeV}}^2$ is found. A sequence of transition curves in the $(\mu ,T)$ plane is obtained for $B$ in the same interval, monotonically decreasing in scale for growing $B$.

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