We show that asymptotic normalization coefficients (ANC) can be extracted from one-nucleon breakup reactions of loosely bound nuclei at 30-300 MeV/nucleon. In particular, the breakup of 8B is described in terms of an extended Glauber model. The 8B ANC extracted from breakup data at several energies and on different targets, C(2)(tot) = 0.450+/-0.039 fm(-1), leads to the astrophysical factor S17(0) = 17.4+/-1.5 eV b for the key reaction for solar neutrino production 7Be(p, gamma)8B. The procedure described provides an indirect method to determine reaction rates of astrophysical interest with beams of loosely bound radioactive nuclei.