In this paper, we present a precise and model-independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Padé approximants. Precise theoretical parametrizations of pion-pion scattering phase shifts based on once—and twice—subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrizations the pole positions of the f0(500) at s=(453±15)-i(297±15)  MeV, the ρ(770) at s=(761.4±1.2)-i(71.8±1.0)  MeV, and the pole of the f2(1270), located at s=(1267.3±1.7)-i(95.0±2.3)  MeV. The couplings of the resonances to two pions are also determined with high precision, obtaining, respectively, 3.8±0.4  GeV, 5.92±0.15 and 4.41±0.23  GeV−1. Special attention is dedicated to the systematic treatment of the theoretical and statistical uncertainties, together with their comparison with previous determinations.