We have used muon-spin rotation, heat capacity and x-ray diffraction measurements in combination with density functional theory and dipole field calculations to investigate the crystal and magnetic structure of FeTi$_2$O$_5$. We observe a long range ordered state below $T_{rm N}$=41.8(5) K with indications of significant correlations existing above this temperature. We determine candidate muon stopping sites in this compound, and find that our data are consistent with the spin Jahn-Teller driven antiferromagnetic ground state with $boldsymbol{k}$=(1/2,1/2,0) reported for CoTi$_2$O$_5$ ($T_{rm N}$=26 K). By comparing our data with calculated dipolar fields we can restrict the possible moment size and directions of the Fe$^{2+}$ ions.
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