We investigate the properties of star-formation-driven outflows by using a large spectroscopic sample of ∼160 000 local "normal" star-forming galaxies drawn from the Sloan digital sky survey (SDSS), spanning a wide range of star formation rates (SFRs) and stellar masses (M∗). The galaxy sample is divided into a fine grid of bins in the M∗-SFR parameter space, for each of which we produced a composite spectrum by stacking the SDSS spectra of the galaxies contained in that bin together. We exploited the high signal-to-noise of the stacked spectra to study the emergence of faint features of optical emission lines that may trace galactic outflows and are otherwise too faint to detect in individual galaxy spectra. We have adopted a novel approach that relies on the comparison between the line-of-sight velocity distribution (LoSVD) of the ionised gas (as traced by the [OIII]λ5007 and Hα+[NII]λλ6548, 6583 emission lines) and the LoSVD of the stars, which are used as a reference for tracing virial motions. Significant deviations in the gas kinematics from the stellar kinematics in the high-velocity tail of the LoSVDs are interpreted as a signature of outflows. Our results suggest that the incidence of ionised outflows increases with SFR and specific SFR. The outflow velocity (vout) is found to correlate tightly with the SFR for SFR> 1 M⊙yr-1, whereas the dependence of vouton SFR is nearly flat at lower SFRs. The outflow velocity appears to also increase with the stellar velocity dispersion (σ∗), although this relation has a much larger scatter than the one with SFR, and we infer velocities as high as vout∼ (6-8)σ∗. Strikingly, we detect the signature of ionised outflows only in galaxies located above the main sequence (MS) of star-forming galaxies in the M∗-SFR diagram, and the incidence of such outflows increases sharply with the offset from the MS. This result suggests that star-formation-driven outflows may be responsible for shaping the upper envelope of the MS by providing a self-regulating mechanism for star formation. Finally, our complementary analysis of the stellar kinematics reveals the presence of blue asymmetries of a few 10 km s-1in the stellar LoSVDs. The origin of such asymmetries is not clear, but a possibility is that they trace the presence of a large number of high velocity runaway stars and hypervelocity stars in radial trajectories in local galaxies.