Background: Although methods and software tools abound for the comparison, analysis, identification, and taxonomic classification of the enormous amount of genomic sequences that are continuously being produced, taxonomic classification remains challenging. The difficulty lies within both the magnitude of the dataset and the intrinsic problems associated with classification. The need exists for an approach and software tool that addresses the limitations of existing alignment-based methods, as well as the challenges of recently proposed alignment-free methods. Results: We combine supervised Machine Learning with Digital Signal Processing to design ML-DSP, an alignment-free software tool for ultrafast, accurate, and scalable genome classification at all taxonomic levels.We test ML-DSP by classifying 7,396 full mitochondrial genomes from the kingdom to genus levels, with 98% classification accuracy. Compared with the alignment-based classification tool MEGA7 (with sequences aligned with either MUSCLE, or CLUSTALW), ML-DSP has similar accuracy scores while being significantly faster on two small benchmark datasets (2,250 to 67,600 times faster for 41 mammalian mitochondrial genomes). ML-DSP also successfully scales to accurately classify a large dataset of 4,322 complete vertebrate mtDNA genomes, a task which MEGA7 with MUSCLE or CLUSTALW did not complete after several hours, and had to be terminated. ML-DSP also outperforms the alignment-free tool FFP (Feature Frequency Profiles) in terms of both accuracy and time, being three times faster for the vertebrate mtDNA genomes dataset. Conclusions: We provide empirical evidence that ML-DSP distinguishes complete genome sequences at all taxonomic levels. Ultrafast and accurate taxonomic classification of genomic sequences is predicted to be highly relevant in the classification of newly discovered organisms, in distinguishing genomic signatures, in identifying mechanistic determinants of genomic signatures, and in evaluating genome integrity.