Aneuploidy is a hallmark of tumor cells, and yet the precise relationship between aneuploidy and a cell’s proliferative ability, or cellular fitness, has remained elusive. In this study, we have combined a detailed analysis of aneuploid clones isolated from laboratory-evolved populations of Saccharomyces cerevisiae with a systematic, genome-wide screen for the fitness effects of telomeric amplifications to address the relationship between aneuploidy and cellular fitness. We found that aneuploid clones rise to high population frequencies in nutrient-limited evolution experiments and show increased fitness relative to wild type. Direct competition experiments confirmed that three out of four aneuploid events isolated from evolved populations were themselves sufficient to improve fitness. To expand the scope beyond this small number of exemplars, we created a genome-wide collection of >1,800 diploid yeast strains, each containing a different telomeric amplicon (Tamp), ranging in size from 0.4 to 1,000 kb. Using pooled competition experiments in nutrient-limited chemostats followed by high-throughput sequencing of strain-identifying barcodes, we determined the fitness effects of these >1,800 Tamps under three different conditions. Our data revealed that the fitness landscape explored by telomeric amplifications is much broader than that explored by single-gene amplifications. As also observed in the evolved clones, we found the fitness effects of most Tamps to be condition specific, with a minority showing common effects in all three conditions. By integrating our data with previous work that examined the fitness effects of single-gene amplifications genome-wide, we found that a small number of genes within each Tamp are centrally responsible for each Tamp’s fitness effects. Our genome-wide Tamp screen confirmed that telomeric amplifications identified in laboratory-evolved populations generally increased fitness. Our results show that Tamps are mutations that produce large, typically condition-dependent changes in fitness that are important drivers of increased fitness in asexually evolving populations.