Sex chromosomes evolved from autosomes many times across the eukaryote phylogeny. Several models have been proposed to explain this transition, some involving male and female sterility mutations linked in a region of suppressed recombination between X and Y (or Z/W, U/V) chromosomes. Comparative and experimental analysis of a reference genome assembly for a double haploid YY male garden asparagus (Asparagus officinalis L.) individual implicates separate but linked genes as responsible for sex determination. Dioecy has evolved recently within Asparagus and sex chromosomes are cytogenetically identical with the Y, harboring a megabase segment that is missing from the X. We show that deletion of this entire region results in a male-to-female conversion, whereas loss of a single suppressor of female development drives male-to-hermaphrodite conversion. A single copy anther-specific gene with a male sterile Arabidopsis knockout phenotype is also in the Y-specific region, supporting a two-gene model for sex chromosome evolution.