A family of four-coordinate FeII complexes formed with N,N'-chelating amido-pyridine ligands was synthesized, and their magnetic properties were investigated. These distorted tetrahedral complexes exhibit significant magnetic anisotropy with zero-field splitting parameter D ranging between -17 and -12 cm-1. Ab initio calculations enabled identification of the structural factors that control the nature of the magnetic anisotropy and the rationalization of the variation of D in these complexes. It is shown that a reduced N-Fe-N angle involving the chelating nitrogen atoms of the ligands is at the origin of the negative D value and that the torsion between the two N-Fe-N planes imposed by steric hindrances further increases the |D| value. Field-induced slow relaxation of magnetization was observed for the three compounds, and a single-molecule magnet behavior with an energy barrier for magnetization flipping (Ueff) of 27 cm-1 could be evidenced for one of them.