We report nonlinear optical characterization of cm-long polycrystalline silicon (poly-Si) waveguides at telecom wavelengths. Laser post-processing of lithographically-patterned amorphous silicon deposited on silica-on-silicon substrates provides low-loss poly-Si waveguides with surface-tension-shaped boundaries. Achieving optical losses as low as 4 dB cm-1 enabled us to demonstrate effects of self-phase modulation (SPM) and two-photon absorption (TPA). Analysis of the spectral broadening and nonlinear losses with numerical modeling reveals the best fit values of the Kerr coefficient n2=4.5×10-18 m W-1 and TPA coefficient βTPA=9.0×10-12 m2 W-1, which are within the range reported for crystalline silicon. On-chip low-loss poly-Si paves the way for flexible integration of nonlinear components in multi-layered photonic systems.