Despite the rapid development of sequencing technologies, the assembly of mammalian-scale genomes into complete chromosomes remains one of the most challenging problems in bioinformatics. To help address this difficulty, we developed Ragout 2, a reference-assisted assembly tool that works for large and complex genomes. By taking one or more target assemblies (generated from an NGS assembler) and one or multiple related reference genomes, Ragout 2 infers the evolutionary relationships between the genomes and builds the final assemblies using a genome rearrangement approach. By using Ragout 2, we transformed NGS assemblies of 16 laboratory mouse strains into sets of complete chromosomes, leaving <5% of sequence unlocalized per set. Various benchmarks, including PCR testing and realigning of long Pacific Biosciences (PacBio) reads, suggest only a small number of structural errors in the final assemblies, comparable with direct assembly approaches. We applied Ragout 2 to the Mus caroli and Mus pahari genomes, which exhibit karyotype-scale variations compared with other genomes from the Muridae family. Chromosome painting maps confirmed most large-scale rearrangements that Ragout 2 detected. We applied Ragout 2 to improve draft sequences of three ape genomes that have recently been published. Ragout 2 transformed three sets of contigs (generated using PacBio reads only) into chromosome-scale assemblies with accuracy comparable to chromosome assemblies generated in the original study using BioNano maps, Hi-C, BAC clones, and FISH.