Aims: Previous studies have found that the Galactic rotation velocity-metallicity (V-[Fe/H]) relations for the thin and thick disk populations show negative and positive slopes, respectively. The first Gaia data release includes the Tycho-Gaia Astrometric Solution (TGAS) information, which we use to analyze the V-[Fe/H] relation for a strictly selected sample with high enough astrometric accuracy. We aim to present an explanation for the slopes of the V-[Fe/H] relationship. Methods: We have identified a sample of stars with accurate Gaia TGAS data and SDSS APOGEE [α/Fe] and [Fe/H] measurements. We measured the V-[Fe/H] relation for thin and thick disk stars classified on the basis of their [α/Fe] and [Fe/H] abundances. Results: We find dV/ d [Fe/H] = -18 ± 2 km s-1 dex-1 for stars in the thin disk and dV/ d [Fe/H] = +23 ± 10 km s-1 dex-1 for thick disk stars, and thus we confirm the different signs for the slopes. The negative value of dV/d[Fe/H] for thin disk stars is consistent with previous work, but the combination of TGAS and APOGEE data provides higher precision, even though systematic errors could exceed ±5 km s-1 dex-1. Our average measurement of dV/d[Fe/H] for local thick disk stars shows a somewhat flatter slope than in previous studies, but we confirm a significant spread and a dependence of the slope on the [α/Fe] ratio of the stars. Using a simple N-body model, we demonstrate that the observed trends for the thick and thin disk can be explained by the measured radial metallicity gradients and the correlation between orbital eccentricity and metallicity in the thick disk. Conclusions: We conclude that the V-[Fe/H] relation for thin disk stars is well determined from our TGAS-APOGEE sample, and a direct consequence of the radial metallicity gradient and the correlation between Galactic rotation and mean Galactocentric distance. Stars formed farther away from the solar circle tend to be near their orbital pericenter, showing larger velocities and on average lower metallicities, while those closer to the Galactic center are usually closer to their orbital apocenter, therefore moving slower and with higher metallicities. The positive dV/d[Fe/H] for the thick disk sample is likely connected to the correlation between orbital eccentricity and metallicity for that population.