Meyer gained his MD from the university in his native city of Cologne in 1924 and his PhD from Berlin University in 1928. He moved to the University of California, Berkeley, in 1930, and in 1933 transferred to the College of Physicians and Surgeons at Columbia, where he has spent the rest of his career. He served as professor of biochemistry from 1954 until his retirement in 1967.

Meyer studied the acidic mucopolysaccharides found in connective tissue and isolated two of these, hyaluronic acid and chondroitin sulfate. He also discovered that various bacteria have enzymes – hyaluronidases – that can break down hyaluronic acid. It was later shown that these enzymes are the same as the ‘spreading factors’ isolated from various sources, such as snake venom and leeches. Meyer and his colleagues found that there are three different types of chondroitin sulfate, and in 1953 he isolated a third mucopolysaccharide, keratosulfate, found in the cornea. This was later also found in cartilage. Meyer also investigated the production and distribution of mucopolysaccharides and was able to show that Marfan's syndrome, an inherited disease of connective tissue, is associated with large amounts of keratosulfate in cartilage.