Genome sizes vary across eukaryotes, largely because of differences in non-coding DNA. However, the physiological effects of this excess DNA are unclear. We engineered budding yeast strains carrying up to 12.8 Mb of predominantly non-coding human DNA, doubling the genome without altering endogenous genes. Genome expansion slowed growth and increased cell size. Spike-in-normalized ChIP-seq and RNA-seq showed that added DNA recruited RNA polymerase II, diverting it from endogenous genes and lowering endogenous mRNA concentration. Ribosome profiling and proteomics revealed little translation from added sequences. A model linked this transcriptional competition to reduced ribosome activity and growth. Thus, excess DNA imposes a fitness cost by sequestering transcriptional resources, providing a mechanistic basis for selection against genome expansion in rapidly proliferating organisms such as yeasts and bacteria.