Using numerical simulations of SU(2) lattice gauge theory we demonstrate from first principles that an external magnetic field leads to spontaneous generation of quark condensates with quantum numbers of electrically charged rho mesons if the strength of the magnetic field exceeds the critical value eB_c = 0.927(77) GeV^2 or B_c =(1.56 \pm 0.13) 10^{16} Tesla. The condensation of the charged $\rho$ mesons in strong magnetic field is a key feature of the recently proposed electromagnetic superconductivity of the vacuum.