Heteromorphic sex chromosomes have evolved repeatedly across diverse species. Suppression of recombination between X and Y chromosomes leads to rapid degeneration of the Y chromosome. However, these early stages of degeneration are not well understood, as complete Y chromosome sequence assemblies have only been generated across a handful of taxa with ancient sex chromosomes. Here we describe the assembly of the threespine stickleback (Gasterosteus aculeatus) Y chromosome, which is less than 26 million years old. Our previous work identified that the non-recombining region between the X and the Y spans ∼17.5 Mb on the X chromosome. Here, we combined long-read PacBio sequencing with a Hi-C-based proximity guided assembly to generate a 15.87 Mb assembly of the Y chromosome. Our assembly is concordant with cytogenetic maps and Sanger sequences of over 90 Y chromosome clones from a bacterial artificial chromosome (BAC) library. We found three evolutionary strata on the Y chromosome, consistent with the three inversions identified by our previous cytogenetic analyses. The young threespine stickleback Y shows convergence with older sex chromosomes in the retention of haploinsufficient genes and the accumulation of genes with testis-biased expression, many of which are recent duplicates. However, we found no evidence for large amplicons found in other sex chromosome systems. We also report an excellent candidate for the master sex-determination gene: a translocated copy of Amh (Amhy). Together, our work shows that the same evolutionary forces shaping older sex chromosomes can cause remarkably rapid changes in the overall genetic architecture on young Y chromosomes.