In all eukaryotic species examined, meiotic recombination, and crossovers in particular, occur non-randomly along chromosomes. The cause for this non-random distribution remains poorly understood but some specific DNA sequence motifs have been shown to be enriched near crossover hotspots in a number of species. We present analyses using machine learning algorithms to investigate whether DNA motif distribution across the genome can be used to predict crossover variation in Drosophila melanogaster, a species without hotspots. Our study exposes a combinatorial non-linear influence of motif presence able to account for a significant fraction of the genome-wide variation in crossover rates at all genomic scales investigated, from 20% at 5-kb to almost 70% at 2,500-kb scale. The models are particularly predictive for regions with the highest and lowest crossover rates and remain highly informative after removing sub-telomeric and -centromeric regions known to have strongly reduced crossover rates. Transcriptional activity during early meiosis and differences in motif use between autosomes and the X chromosome add to the predictive power of the models. Moreover, we show that population-specific differences in crossover rates can be partly explained by differences in motif presence. Our results suggest that crossover distribution in Drosophila is influenced by both meiosis-specific chromatin dynamics and very local constitutive open chromatin associated with DNA motifs that prevent nucleosome stabilization. These findings provide new information on the genetic factors influencing variation in recombination rates and a baseline to study epigenetic mechanisms responsible for plastic recombination as response to different biotic and abiotic conditions and stresses.