Chromosome-scale genome sequence assemblies underpin pan-genomic studies. Recent genome assembly efforts in the large-genome Triticeae crops wheat and barley have relied on the commercial closed-source assembly algorithm DeNovoMagic. We present TRITEX, an open-source computational workflow that combines paired-end, mate-pair, 10X Genomics linked-read with chromosome conformation capture sequencing data to construct sequence scaffolds with megabase-scale contiguity ordered into chromosomal pseudomolecules. We evaluate the performance of TRITEX on publicly available sequence data of tetraploid wild emmer and hexaploid bread wheat, and construct an improved annotated reference genome sequence assembly of the barley cultivar Morex as a community resource.