The genomic alterations associated with cancers are numerous and varied, involving both isolated and large-scale complex genomic rearrangements (CGRs). Although the underlying mechanisms are not well understood, CGRs have been implicated in tumorigenesis. Here, we introduce CouGaR a novel method for characterizing the genomic structure of amplified CGRs leveraging both depth-of-coverage and discordant pair-end mapping techniques. We applied our method to WGS samples from The Cancer Genome Atlas and identify amplified CGRs in at least 5.2% (10+ copies) to 17.8% (6+ copies) of the samples. Furthermore, ~95% of these amplified CGRs contain genes previously implicated in tumorigenesis, indicating the importance and widespread occurrence of CGRs in cancers. Additionally, CouGaR identified the occurrence of chromoplexy in nearly 63% of all prostate cancer samples and 30% of all bladder cancer samples. To further validate the accuracy of our method, we experimentally tested 17 predicted fusions in two pediatric glioma samples and validated 15 of these (88%) with precise resolution of the breakpoints via qPCR experiments and Sanger sequencing, with nearly perfect copy count concordance. Additionally, to further help display and understand the structure of CGRs we have implemented CouGaR-viz, a generic standalone tool for visualization of amplified fusion that allows us to visualize the copy count of regions, breakpoints, and relevant genes.