We report the observation of spin glass state in the double perovskite oxide Sr$_{2}$FeCoO$_{6}$ prepared through sol-gel technique. Initial structural studies using x rays reveal that the compound crystallizes in tetragonal $I 4/m$ structure with lattice parameters, $a$ = 5.4609(2) Å and $c$ = 7.7113(7) Å. The temperature dependent powder x ray studies reveal no structural phase transition in the temperature range 10 -- 300 K. However, the unit cell volume shows an anomaly coinciding with the magnetic transition temperature thereby suggesting a close connection between lattice and magnetism. Neutron diffraction studies and subsequent bond valence sums analysis show that in Sr$_{2}$FeCoO$_{6}$, the $B$ site is randomly occupied by Fe and Co in the mixed valence states of Fe$^{3+}$/Fe$^{4+}$ and Co$^{3+}$/Co$^{4+}$. The random occupancy and mixed valence sets the stage for inhomogeneous magnetic exchange interactions and in turn, for the spin glass like state in this double perovskite which is observed as an irreversibility in temperature dependent dc magnetization at $T_f∼$ 75 K. Thermal hysteresis observed in the magnetization profile of Sr$_{2}$FeCoO$_{6}$ is indicative of the mixed magnetic phases present. The dynamic magnetic susceptibility displays characteristic frequency dependence and confirms the spin glass nature of this material. Dynamical scaling analysis of $χ'(T)$ yields a critical temperature $T_{ct}$ = 75.14(8) K and an exponent $zν$ = 6.2(2) typical for spin glasses. The signature of presence of mixed magnetic interactions is obtained from the thermal hysteresis in magnetization of Sr$_{2}$FeCoO$_{6}$. Combining the neutron and magnetization results of Sr$_2$FeCoO$_6$, we deduce the spin states of Fe to be in low spin while that of Co to be in low spin and intermediate spin. ; Comment: 23 pages, 6 figures, accepted in J. Appl. Phys