Born in Greenville, South Carolina, Rose was educated at Davidson College, North Carolina, and at Yale, where he obtained his PhD in 1911. He taught at the University of Texas from 1913 to 1922, when he moved to the University of Illinois as professor of physiological chemistry; from 1936 until his retirement in 1955 he was professor of biochemistry there.

In the late 1930s Rose was responsible for a beautifully precise set of experiments that introduced the idea of an essential amino acid into nutrition, demonstrating its effect on both human and rodent diet. It had been known for a long time to nutritionists that rats fed on a diet in which the only protein was zein (found in corn), despite enrichment with vitamins, would inevitably die. Rose worked with the constituent amino acids rather than proteins; he still found, however, that whatever combination of amino acids he tried the rats died. However, if the milk protein, casein, was added to their diet the ailing rats recovered.

It was obvious from this that casein must contain an amino acid, not present in zein and then unknown, that was essential for life. Rose began a long series of experiments extracting and testing various fragments of casein until at last he found, in 1936, threonine, the essential amino acid that provided a satisfactory rodent diet when added to the other amino acids. Rose argued that if there was one essential amino acid there could well be others. Over several years he therefore continued to manipulate the rodent diet and finally established the primary importance of ten amino acids: lysine, tryptophan, histidine, phenylalanine, leucine, isoleucine, methionine, valine, and arginine, in addition to the newly discovered threonine. With these in adequate quantities the rats were capable of synthesizing any of the other amino acids if and when they were needed.

In 1942 Rose began a ten-year research project on human diet. By persuading students to restrict their diet in various ways Rose eventually established that there are eight essential amino acids for humans: unlike rats we can survive without arginine and histidine. Since then, however, it has been suggested that these two amino acids are probably required to sustain growth in infants.