The evolution of magnetic order in Fe1+ySexTe1-x crystals as a function of Se content was investigated by means of ac/dc magnetometry and muon-spin spectroscopy. Experimental results and self-consistent density functional theory calculations both indicate that muons are implanted in vacant iron-excess sites, where they probe a local field mainly of dipolar origin, resulting from an antiferromagnetic (AFM) bicollinear arrangement of iron spins. This long-range AFM phase becomes progressively disordered with increasing Se content. At the same time all the tested samples manifest a marked glassy character that vanishes for high Se contents. The presence of local electronic/compositional inhomogeneities most likely favours the growth of clusters whose magnetic moment 'freezes' at low temperature. This glassy magnetic phase justifies both the coherent muon precession seen at short times in the asymmetry data, as well as the glassy behaviour evidenced by both dc and ac magnetometry.