The compound he had placed in the cage was dichlorodiphenyltrichloroethane (DDT), or, more precisely, 1,1,1-trichloro-2,2-bis(4-chlorophenyl)ethane, which a Viennese Pharmacologist named Othmar Zeidler had first synthesized in 1874. Zeidler, while publishing a paper about his synthesis, had not investigated the properties of the new compound, and had thus failed to recognize its extraordinary value as an insecticide.

Müller was born on January 12, 1899 in Olten, Solothurn to Gottlieb and Fanny (née Leypoldt or Leypold) Müller. He was the oldest of four children. His Father worked for the Swiss Federal Railways and the family first moved to Lenzburg in Aargau and then to Basel.

In 1916 he left school to work as a laboratory assistant at Dreyfus (or Dreyfuss & Cie) and Company; the next year he became an assistant Chemist in the Scientific-Industrial Laboratory of the electrical plant of Lonza A.G. Returning to school in 1918, he obtained his diploma by 1919 and entered Basel University in the same year.

At Basel University he studied chemistry (with a minor in botany and physics) and started to study inorganic chemistry under professor Friedrich Fichter. In 1922 he continued his studies in the organic chemistry lab of Hans Rupe. While working for Rupe as assistant, he received his PhD writing a dissertation entitled Die chemische und elektrochemische Oxidation des as. m-Xylidins und seines Mono- und Di-Methylderivates (The Chemical and Electrochemical Oxidation of Asymmetrical m-Xylidene and its Mono- and Di-methyl Derivatives) in 1925. He graduated with summa cum laude.

On 25 May 1925 Müller began working as a research Chemist for the dye division of J. R. Geigy AG in Basel. His first research topics at Geigy concerned synthetic and plant-derived dyes and natural tanning agents. This work led to the production of the synthetic tanning agents Irgatan G, Irgatan FL and Irgatan FLT.

Müller married Friedel Rüegsegger in 1927 and had two sons, Heinrich (b. 1929) and Niklaus (b. 1933), and one daughter, Margaretha (b. 1934). In his free time, Müller liked the nature in the Swiss alps and in the Swiss Jura where he owned a small holiday home. Furthermore, he liked to photograph and owned a small fruit farm.

In embracing this goal, Müller was motivated by two events. The first of these was a major food shortage in Switzerland, which underscored the need for a better way to control the infestation of crops by insects. The second was the typhus epidemic in Russia, which was the most extensive and lethal such epidemic in history. He began his search for his insecticide in 1935.

He studied all the data he could find on the subject of insecticides, decided which chemical properties the kind of insecticide he was in search of would exhibit, and set out to find a compound that would suit his purposes. Müller spent four years searching and failed 349 times before, in September 1939, he found the compound he was looking for. He placed a fly in a cage laced with one particular compound, and short while later, the fly died.

After taking out a Swiss patent on DDT in 1940 (a U.K. patent followed in 1942 and patents in the U.S. and Australia in 1943), Geigy began to market two DDT-based products, a 5% dust called Gesarol spray insecticide and a 3% dust called Neocid dust insecticide. The name DDT was first employed by the British Ministry of Supply in 1943, and the product was added to U.S. Army supply lists in May of the same year. It was also in 1943 that the first practical tests of DDT as a residual insecticide against adult vector mosquitoes were carried out. The next year, in Italy, tests were performed in which residual DDT was applied to the interior surfaces of all habitations and outbuildings of a community to test its effect on Anopheles vectors and malaria incidence.

Müller became Geigy's Deputy Director of Scientific Research on Substances for Plant Protection in 1946. In 1948 he was awarded the Nobel Prize in Physiology and Medicine, "for his discovery of the high efficiency of DDT as a contact poison against several arthropods." The fact that he was accorded this honor even though he was neither a physician nor a medical researcher reflected the immense impact that DDT had had in the fight against human disease. The Nobel Committee said: "DDT has been used in large quantities in the evacuation of concentration camps, of prisons and deportees. Without any doubt, the material has already preserved the life and health of hundreds of thousands." In 1951, Müller was one of seven Nobel Laureates who attended the 1 Lindau Nobel Laureate Meeting.

In addition to the 1948 Nobel Prize in physiology or Medicine, Müller received an honorary doctorate from the University of Thessalonica in Greece in recognition of DDT's impact on the Mediterranean region. He retired from Geigy in 1961, continuing his research in a home laboratory.

DDT saved the lives of millions during World War II. Between the 1950s and 1970s, DDT helped eradicate malaria entirely from many countries, the U.S. included.

Müller received many honors in his life, among them the Nobel Prize in Physiology or Medicine. Specifically Greece honored him for the near elimination of malaria in the country as a result of his discovery. In 1963, he was invited to Greece and received with great sympathy and celebrated as national hero.

He died in the early morning of October 13, 1965 in Basel after a short illness.

During the course of his research, Müller found that insects absorbed chemicals differently than mammals. This led him to believe it likely that there are chemicals toxic exclusively to insects. He sought to "synthesize the ideal contact insecticide—one which would have a quick and powerful toxic effect upon the largest possible number of insect species while causing little or no harm to plants and warm-blooded animals." He also made it his goal to create an insecticide that was long-lasting and cheap to produce, along with a high degree of chemical stability.