The spectra of charged and neutral $\rho$ and $\pi$ mesons in the framework of the vacuum correlator method obtained from the relativistic Hamiltonian in external homogeneous magnetic field (MF). The spectra of all 12 spin-isospin s-wave states generated by $q \bar{q}$ light mesons with different spin projections are calculated analytically as a function of the field strength. Three types of the asymptotic behaviour in strong field limit are found: two of them grow with MF and the last one tend to be a constant (zero mode). The mass of the zero mode becomes small in MF whcih can be the source of the meson collapse. The potential collapse has two different sources -- colormagnetic hyperfine interaction and one-gluon exchange and it doesn't occur for the MF $eB < 2 \ GeV^2$. The results are in agreement with recent lattice calculations.