The biochemist Frederick Sanger, who has died aged 95, had the rare distinction of winning the Nobel prize twice (in 1958 and 1980), placing him in the company of Marie Curie, Linus Pauling and John Bardeen. Sanger's work, first on the insulin molecule and then on DNA, opened the door to a new era of medicine and biology, especially in the application of genetic engineering. He transformed the field of genetics from a science of descriptive analysis into today's powerful technology of genetic manipulation and gene therapy.

Sanger solved what had been seemingly intractable problems posed by the sheer size and complexity of the two principal molecules of life that govern our health and destiny – proteins and the nucleic acids DNA and RNA. He was the first to reveal the structure of a protein, which happened to be insulin. The discovery was an essential step for the laboratory synthesis of insulin and a major advance in the treatment of diabetes. It opened a floodgate of research into the way hundreds of proteins conspired to create and sustain a living organism. Sanger referred to proteins as the machinery of living matter.

He then turned his skills on teasing out the chemical composition of the individual genes contained in DNA. His group was the first to work out the precise composition of the entire genome of any organism when they figured out the structure of the DNA of the virus Phi X 174. Although the virus was a relatively modest life form, it nevertheless contained 5,400 of the chemical bases that link together in chains in the creation of DNA. The Sanger Sequencing Method for decoding the structure of DNA was the main technique used in 1990 for the Human Genome Project, the massive research effort aimed at discovering the composition of every one of the thousands of human genes.

Sanger was born in Rendcomb, Gloucestershire, to Frederick, a doctor, and his wife, Ciceley. His father encouraged his interest in biology. Sanger went to Bryanston school, Dorset, and won a scholarship to study science at St John's College, Cambridge. He was attracted to biochemistry by the sheer excitement for the subject shared by the relatively young members of the department working under Frederick Gowland Hopkins, a Nobel prizewinner who had discovered vitamins. Sanger graduated in 1939 and then did an advanced course in biochemistry. As a Quaker, he was a conscientious objector during the second world war. He stayed at Cambridge and divided his time between studying for a PhD and carrying out applied research into nitrogen uptake in potatoes.

Sanger completed his doctorate in 1943 and joined a research group organised by AC Chibnall to work on proteins. A revolution in analytical chemistry was under way, started by two British biochemists, Archer Martin and Richard Synge. They had developed a technique called partition chromatography, which made possible the separation and purification of huge molecules such as proteins and nucleic acids.

While proteins were known to consist of large numbers of amino acids, the basic chemical building blocks of life, the details remained a mystery of how many amino acids there were of each kind and how they were arranged in a particular molecule. When Chibnall first tried to get Sanger a grant from the Medical Research Council to work on protein structure, the grant was refused because it was believed that the pattern of amino acids in a protein was simply random. Nevertheless, a smaller grant was obtained. When Sanger started work he chose to study insulin because of its medical implications and because there was a plentiful supply of the bovine variety. He perfected a way of unravelling the complete amino acid sequence of even the most complex of proteins.

He came up with a technique using a special marking agent, now known as Sanger's reagent, for breaking the long chains of amino acids in protein molecules into short fragments. He then worked out their constitution and gradually pieced together the structure of the whole molecule. Sanger spent 10 years carefully identifying small fragments of the insulin molecule and working out their composition to arrive at its structure. By 1953 he not only had the exact sequence of amino acids for insulin, but had also shown the precise but quite small differences that existed between the insulin of different mammalian species. For this work he won the 1958 Nobel prize in chemistry outright.

The discovery was especially striking because it showed that a protein was a unique sequence of amino acids that gave it a distinct three-dimensional structure upon which its properties depended. Once the structure of proteins became known, it was then possible to ask how were they made.

In the early 1960s, Sanger became a senior member at the Medical Research Council's new laboratory for molecular biology in Cambridge where, under the guidance of Max Perutz, a trailblazing team of scientists including Francis Crick and James Watson were researching the physical structure of large proteins and the genetic nucleic acids DNA and RNA. Once Crick and Watson had produced an explanation for how the genetic code was inherited through DNA, it was inevitable that Sanger should apply his flair in amino acid sequencing to deciphering the detailed construction of individual genes. Sanger said in his Nobel lecture in 1980 that it was the coded amino acid sequences within specific sections of the strands of DNA that conveyed the genetic information. Those sequences were as much the stuff of genes as the DNA helix.

The sheer size of the DNA molecule called for subtler techniques than those that cracked the structure of insulin. Sanger decided to create short fragments of the genetic material of DNA so those fragments might be recombined to create modified genes. The potential value of such a technique in treating genetic disease, for example, was already foreseeable.

Sanger and his team – which included Bart Barrell, Alan Coulson and George Brownlee – sought ever-improving methods for sequencing DNA and RNA. The fundamental methods of "reading" DNA using special bases called chain terminators, very thin gel systems, and the adaptation of cloning methods to produce DNA strands, were developed by the group. After Sanger produced the first DNA whole genome sequence for the virus Phi X 174, he sequenced the first human genome in the shape of the DNA in mitochondria – small energy factories in all our cells.

Sanger shared the Nobel prize for chemistry in 1980 with Walter Gilbert at Harvard, for their contributions concerning the determination of base sequences in nucleic acids, and with Paul Berg at Stanford, who demonstrated the way of recombining DNA segments that made genetic engineering a practical proposition.

Sanger retired in 1983 and devoted himself to his garden in the Cambridge fens, exchanged his laboratory bench for one of a cabinetmaker, and pottered about on the river. He refused a knighthood but accepted an OM in 1986. The Sanger Centre (which became the Sanger Institute), was opened in 1993 to continue his work in DNA sequencing.

Sanger married Margaret Joan Howe in 1940. They had two sons and a daughter.

• Frederick Sanger, biochemist, born 13 August 1918; died 19 November 2013

• Pearce Wright died in 2005