A detailed understanding of the genome-wide variability of single-nucleotide germline mutation rates is essential to studying human genome evolution. Here, we use ~36 million singleton variants from 3560 whole-genome sequences to infer fine-scale patterns of mutation rate heterogeneity. Mutability is jointly affected by adjacent nucleotide context and diverse genomic features of the surrounding region, including histone modifications, replication timing, and recombination rate, sometimes suggesting specific mutagenic mechanisms. Remarkably, GC content, DNase hypersensitivity, CpG islands, and H3K36 trimethylation are associated with both increased and decreased mutation rates depending on nucleotide context. We validate these estimated effects in an independent dataset of ~46,000 de novo mutations, and confirm our estimates are more accurate than previously published results based on ancestrally older variants without considering genomic features. Our results thus provide the most refined portrait to date of the factors contributing to genome-wide variability of the human germline mutation rate.