Strontium clusters of size 2 to 20 atoms have been studied within the local density approximation using the ab-initio molecular dynamics method with a plane wave basis in which the s and p electron wavefunctions are well represented. The resulting low lying isomers are optimized using a full-potential linear muffin tin orbital method which treats the d-electrons also on an equal footing. We find that the d electrons contribute significantly to the binding energy as the cluster size grows, expedite the onset of metallicity and induce icosahedral growth. These results are in complete agreement with the experimental finding of rare-gas like magic clusters of group IIA elements and suggest that the observation of icosahedral growth in some transition metal clusters may have a similar origin.