Agarose hydrogels are poroviscoelastic materials that exhibit a waterlogged-crosslinked microstructure. Despite an extensive use in biotechnologies and numerous studies of the elastic properties of agarose gels, little is known about the compressible behavior and the microstructural changes of such fibrillar hydrogels under compression. The present work investigates the mechanical response of centimeter-sized pre-molded agarose cylinders when applying a compressive strain ramp over an extended range of loading speed and polymer concentration. One of the original contributions is the simultaneous monitoring of the changes in the hydrogel volume to determine the Poisson’s ratio through a spatiotemporal method. The linear poroelastic response of agarose hydrogels shows a compressible behavior at strain rates less than 0.7 % s−1. The critical compressive strain of a few percent at the onset of the non-linear regime and the always positive Poisson’s ratio decrease when applying a slow compressive ramp. The mechanical response in the linear regime is typical of a deformation mode either dominated by the bending of semiflexible strands (enthalpic regime) or by the stretching of the network (entropic regime) at higher agarose concentration. Cyclic linear shear deformations superimposed to a compressive strain from 0.5 up to 40% further give evidence of a compression-softening of the network causing the transition to the non-linear regime without dependence upon the network topology and connectivity. Finally, the buckling-induced aging of the network under a weak compression and the poroviscoelasticity of the hydrogel are shown to impact the relaxation of the normal stress and the equilibrium stress.