A magnesium halide adduct represented by the formula (I): MgX2.mROH.nE.pH2O, in which X is chlorine, bromine, a C1-C12 alkoxy, a C3-C10 cycloalkoxy or a C6-C10 aryloxy, with the proviso that at least one X is chlorine or bromine; R is a C1-C12 alkyl, a C3-C10 cycloalkyl or a C6-C10 aryl; E is an o-alkoxybenzoate compound represented by the formula (II): in which R1 and R2 groups are independently a C1-C12 linear or branched alkyl, a C3-C10 cycloalkyl, a C6-C10 aryl, a C7-C10 alkaryl or an C7-C10 aralkyl, the R1 and R2 groups are identical to or different from the R group; m is in a range of from 1.0 to 5.0; n is in a range of from 0.001 to 0.5; and p is in a range of from 0 to 0.8, is disclosed. A catalyst component useful in olefin polymerization, which comprises a reaction product of (1) the magnesium halide adduct, (2) a titanium compound, and optionally (3) an electron donor compound, is also disclosed.