With initial and final particles on-shell, the anomalous weak-magnetic dipole moments of b and c quarks are electroweak gauge invariant quantities of the effective couplings Zb b and Zc c , respectively, and good candidates to test the Standard Model and/or new physics. Here we present a complete computation of these quantities within the Standard Model. We show that decoupling properties with respect to heavy particles do take place in the weak magnetic moment. The obtained values, a b ( M Z 2) = (2.98 − 1.56 i) × 10 −4 and a c ( M Z 2) = (−2.80 + 1.09 i) × 10 −5 are dominated by one-gluon exchange diagrams. The electroweak corrections are less than 1% of the total magnitude.