The magnetic ground state of B-site ordered double perovskite Sr2DyRuO6 has been investigated using muon spin rotation and relaxation (µSR), neutron powder diffraction (NPD) and inelastic neutron scattering (INS), in addition to heat capacity and magnetic susceptibility (ac and dc) measurements. A clear signature of a long-range ordered magnetic ground state has been observed in the heat capacity data, which exhibit two sharp anomalies at 39.5 and 36 K found as well in the magnetic data. Further confirmation of long-range magnetic ordering comes from a sharp drop in the muon initial asymmetry and a peak in the relaxation rate at 40 K, along with a weak anomaly near 36 K. Based on temperature dependent NPD, the low temperature magnetic structure contains two interpenetrating lattices of Dy 3+ and Ru 5+ , forming an antiferromagnetic ground state below 39.5 K with magnetic propagation vector k = (0,0,0). The magnetic moments of Dy 3+ and Ru 5+ at 3.5 K are pointing along the crystallographic b-axis with values of µ Dy = 4.92(10) µB and µ Ru = 1.94(7) µB, respectively. The temperature dependence of the Ru 5+ moments follows a mean field type behaviour, while that of the Dy 3+ moments exhibits a deviation indicating that the primary magnetic ordering is induced by the order of the 4d-electrons of Ru 5+ rather than that of its proper 4f-Dy 3+ electrons. The origin of the second anomaly observed in the heat capacity data at 36.5 K must be connected to a very small spin reorientation as the NPD studies do not reveal any clear change in the observed magnetic Bragg peaks' positions or intensities between these two transitions. INS measurements reveal the presence of crystal field excitations (CEF) in the paramagnetic state with overall CEF splitting of 73.8 meV, in agreement with the point change model calculations, and spin wave excitations below 9 meV at 7 K. Above TN, the spin wave excitations transform into a broad diffuse scattering indicating the presence of short-range dynamic magnetic correlations.