Enhancers change rapidly during evolution, but the mechanism by which new enhancers originate in the genome is mostly unknown. Using ChIP-seq data across mammalian species and multiple tissue-types, we find that germline DNA replication time is tightly associated with the emergence of new enhancers. While enhancers are most common in euchromatic regions, new enhancers emerge almost twice as often in late compared to early replicating regions, independent of transposable elements. New enhancers appear to be largely neutrally evolving based on human population genetics data. They are also enriched in eQTLs and are more tissue-specific than evolutionarily conserved enhancers. Accordingly, genes that bind to these enhancers, inferred by their binding sequences, are also more recently evolved and more tissue-specific in gene expression. A similar relationship between enhancer turnover and DNA replication time is also observed in cancer. Mutation rates are consistently elevated in enhancers that have experienced turnover regardless of replication time strongly suggesting that mutations are a causal mechanism. Finally, we show that the nucleotides biases associated with replication timing have a profound impact on the classes of transcription factors that bind at mammalian enhancers. Taken together, these results demonstrate similar effects of chromatin context on enhancer evolution across multiple time scales, suggesting these observations are time-invariant principles of genome evolution.