A few years ago I used to see a lot more of that sort of thing, and I'm remembering a particular favorite Christmas one I had. From what I recall, the block and shirt were usually just fused together with interfacing and an applique or small zigzag stitch was used to hold down the edges. Often, the edges would be sealed with puffy paint type products.
Keep in mind that the normal outer seam allowance would need to be trimmed down some to give the proper look.
There are a number of modern videos and techniques. A quick google on "sweatshirt with quilt block" brought up all sorts of instructional sites and pictures.