Prof Dame Sally Davies says in her annual report that the NHS must deliver her "genomic dream" within five years.
Over 31,000 NHS patients, including some with cancer, have already had their entire genetic code sequenced.
Dame Sally wants whole genome sequencing (WGS) to become as standard as blood tests and biopsies.
Humans have about 20,000 genes - bits of DNA code or instructions that control how our bodies works.
Tiny errors in this code can lead to cancer and other illnesses.
Sometimes these mistakes are inherited from a parent, but most of the time they happen in previously healthy cells.
WGS - which costs about £700 - can reveal these errors by comparing tumour and normal DNA samples from the patient.
Dame Sally says that in about two-thirds of cases, this information can then improve their diagnosis and care.
Doctors can tailor treatments to the individual, picking the drugs mostly likely to be effective.
And WGS can also show which patients are unlikely to benefit, so they can avoid having unnecessary drugs and unpleasant side-effects.
Dame Sally wants DNA testing to become standard across cancer care, as well as some other areas of medicine, including rare diseases and infections.
"I want the NHS across the whole breadth to be offering genomic medicine - that means diagnosis of our genes - to patients where they can possibly benefit," her report says.
People with rare diseases could benefit from having greater access to the technology, speeding up diagnosis.
Doctors are already using genetic tests to identify and better treat different strains of the infectious disease tuberculosis.
Dame Sally said patients could be assured that their genetic data would be stored securely and "de-identified" so that their privacy would be protected.
Over 10 years ago, international scientists reached a breakthrough in DNA work - sequencing the entire genetic blueprint of man. The Human Genome Project meant experts now had a catalogue of DNA code to explore and refer to.
They began to understand which genes controlled which processes in the body and how these could go wrong.
Doctors then started to "read" a patient's DNA to get a better idea of what might be causing their symptoms and how best to treat their illness.
Genomic medicine - tailoring care based on an individual's unique genetic code - is now transforming the way people are cared for by the NHS.
Genes can predict if a woman with breast cancer might respond to certain drugs, or whether radiotherapy is likely to shrink a tumour, for example.
Currently, genetic testing of NHS patients in England is done at 25 regional laboratories, as well as some other small centres.
Dame Sally wants to centralise the service and set up a national network to ensure equal access to the testing across the country.A new National Genomics Board would be set up, chaired by a minister, to oversee the expansion and development of genomic services.
Dame Sally told BBC Breakfast that a lot of money was being spent because it was currently operating like a "cottage industry".
By having centralised laboratories, more could be done with the money, including keeping up with the latest technology, she said.
She said one obstacle could be doctors themselves, who "don't like change", and she urged cancer service patients to press their doctors to move from a local to a national service.
She also said patients must understand they needed to allow use of their data, alongside other data, in order to get the best diagnosis, and therefore the best treatment.
Phil Booth, from campaigning organisation, MedConfidential, said this move had "huge potential" for patients and the NHS, but there were "great risks with large collections of sensitive data".
"Every single use of patient data must be consensual, safe and transparent," he told BBC Radio Four's Today programme, and patients should be able to opt-out if they so wish.