We measure the mass difference Delta m(0) between the D*(2010)(+) and the D-0 and the natural linewidth Gamma of the transition D*(2010)(+) -> D-0 pi(+). The data were recorded with the BABAR detector at center-of-mass energies at and near the gamma(4S) resonance, and correspond to an integrated luminosity of approximately 477 fb(-1). The D-0 is reconstructed in the decay modes D-0 -> K-pi(+) and D-0 -> K-pi(+) and D-0 -> K-pi(+)pi(-)pi(+). For the decay mode D-0 -> K-pi(+) we obtain Gamma = (83.4 +/- 1.7 +/- 1.5) keV and Delta m(0) = (145425.6 +/- 0.6 +/- 18) keV, where the quoted errors are statistical and systematic, respectively. For the D-0 -> K-pi(+)pi(-)pi(+) mode we obtain Gamma = (83.2 +/- 1.5 +/- 2.6) keV and Delta m(0) = (145426.6 +/- 0.5 +/- 2.0) keV. The combined measurements yield Gamma = (83.3 +/- 1.2 +/- 1.4) keV and Delta m(0) (145425.9 +/- 0.4 +/- 1.7) keV; the width is a factor of approximately 12 times more precise than the previous value, while the mass difference is a factor of approximately 6 times more precise.