Background: Heteromorphic sex chromosomes have evolved repeatedly across diverse species. Suppression of recombination between X and Y chromosomes leads to degeneration of the Y chromosome. The progression of degeneration is not well understood, as complete sequence assemblies of heteromorphic Y chromosomes have only been generated across a handful of taxa with highly degenerate sex chromosomes. Here, we describe the assembly of the threespine stickleback (Gasterosteus aculeatus) Y chromosome, which is less than 26 million years old and at an intermediate stage of degeneration. Our previous work identified that the non-recombining region between the X and the Y spans approximately 17.5 Mb on the X chromosome. Results: We combine long-read 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 BAC clones. We find three evolutionary strata on the Y chromosome, consistent with the three inversions identified by our previous cytogenetic analyses. The threespine stickleback Y shows convergence with more degenerate 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 find no evidence for large amplicons identified in other sex chromosome systems. We also report an excellent candidate for the master sex-determination gene: a translocated copy of Amh (Amhy). Conclusions: Together, our work shows that the evolutionary forces shaping sex chromosomes can cause relatively rapid changes in the overall genetic architecture of Y chromosomes.