  We predict the amplitude of the $B\to K \ell^+\ell^-$ decay in the region of
the dilepton invariant mass squared $0<q^2\leq m_{J/\psi}^2$, that is, at large
hadronic recoil. The $B\to K$ form factors entering the factorizable part of
the decay amplitude are obtained from QCD light-cone sum rules. The nonlocal
effects, generated by the four-quark and penguin operators combined with the
electromagnetic interaction, are calculated at $q^2<0$, far below the hadronic
thresholds. For hard-gluon contributions we employ the QCD factorization
approach. The soft-gluon nonfactorizable contributions are estimated from QCD
light-cone sum rules. The result of the calculation is matched to the hadronic
dispersion relation in the variable $q^2$, which is then continued to the
kinematical region of the decay. The overall effect of nonlocal contributions
in $B\to K\ell^+\ell^-$ at large hadronic recoil is moderate. The main
uncertainty of the predicted $B\to K \ell^+\ell^-$ partial width is caused by
the $B\to K$ form factors. Furthermore, the isospin asymmetry in this decay is
expected to be very small. We investigate the deviation of the observables from
the Standard Model predictions by introducing a generic new physics
contribution to the effective Hamiltonian.
