The major DNA constituent of primate centromeres is alpha satellite DNA. As much as 2%-5% of sequence generated as part of primate genome sequencing projects consists of this material, which is fragmented or not assembled as part of published genome sequences due to its highly repetitive nature. Here, we develop computational methods to rapidly recover and categorize alpha-satellite sequences from previously uncharacterized whole-genome shotgun sequence data. We present an algorithm to computationally predict potential higher-order array structure based on paired-end sequence data and then experimentally validate its organization and distribution by experimental analyses. Using whole-genome shotgun data from the human, chimpanzee, and macaque genomes, we examine the phylogenetic relationship of these sequences and provide further support for a model for their evolution and mutation over the last 25 million years. Our results confirm fundamental differences in the dispersal and evolution of centromeric satellites in the Old World monkey and ape lineages of evolution.