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The effect of structural relaxation and interfacial oxidation is demonstrated from first principles to have a crucial impact on interlayer exchange coupling (IEC) in crystalline Fe| MgO| Fe magnetic tunnel junctions (MTJs). It is shown that the IEC becomes antiferromagnetic for the relaxed structure in contrast to ferromagnetic for unrelaxed Fe| MgO| Fe MTJs. Furthermore, the antiferromagnetic IEC is strongly enhanced in the presence of oxygen vacancies while it is decreased by overoxidation and may even become ferromagnetic for sufficiently high oxygen concentration at the Fe∣ MgO interface. These results were supported using a tight-binding model and provide an explanation for recent experimental studies.