Natural and synthetic hydrogel scaffolds exhibit distinct viscoelastic properties at various length scales and deformation rates. Laser Speckle Rheology (LSR) offers a novel, non-contact optical approach for evaluating the frequency-dependent viscoelastic properties of hydrogels. In LSR, a coherent laser beam illuminates the specimen and a high-speed camera acquires the time-varying speckle images. Cross-correlation analysis of frames returns the speckle intensity autocorrelation function, g2(t), from which the frequency-dependent viscoelastic modulus, G*(ω), is deduced. Here, we establish the capability of LSR for evaluating the viscoelastic properties of hydrogels over a large range of moduli, using conventional mechanical rheometry and atomic force microscopy (AFM)-based indentation as reference-standards. Results demonstrate a strong correlation between |G*(ω)| values measured by LSR and mechanical rheometry (r = 0.95, p < 10-9), and z-test analysis reports that moduli values measured by the two methods are identical (p > 0.08) over a large range (47 Pa - 36 kPa). In addition, |G*(ω)| values measured by LSR correlate well with indentation moduli, E, reported by AFM (r = 0.92, p < 10-7). Further, spatially-resolved moduli measurements in micro-patterned substrates demonstrate that LSR combines the strengths of conventional rheology and micro-indentation in assessing hydrogel viscoelastic properties at multiple frequencies and small length-scales.