In 1994 Borst became minister of Health for the Democrats 66 in the First cabinet of Wim Kok. As a minister, Borst was known for two things, for introducing progressive legislation in medical ethics and for her attempts to reform the medical system to better cope with the aging population.
In 2001 she implemented a law legalizing Euthanasia in the Netherlands under certain extraordinary conditions, and only when extensive protocols had been followed by the physician, and subject to an obligation of full reporting to a governing body. The law (Dutch: de Wet Toetsing levensbeëindiging en hulp bij zelfdoding, law on the legal review of euthanasia and assisted suicide) is considered her most important contribution in politics.
Other progressive decisions she is responsible for include:
In 1994 she strengthened the rights of patients, giving them the right to information and privacy, and the explicit right to refuse treatment.
In 1996 she implemented the law on organ donation. As a result of the law, all Dutch citizens are asked when whether they wanted to become organ donor when they are 18 years old.
In 2001 the law on foetal tissue was passed, which legalized the scientific use of foetal tissue for medical research applications, if the parents agreed and if the foetal tissue was the result of an abortion or miscarriage.
She faced political problems preparing the Dutch medical system for the aging of the population. An important part of her reforms of the medical system was to integrate the health insurance system (which had a public and private part), achieving that all citizens would pay the same amount for the same coverage. Although her ministry's budget was drastically increased during this period, she still had to limit the budgets of the hospitals. This led to a problem of long waiting lists for simple medical procedures. From both the political left and the political right she was criticized for what was seen as her mismanagement of the medical system.
After the parliamentary inquiry in the El Al Flight 1862 (Bijlmer Plane Crash), Borst faced a motion of no confidence in June 1999. The inquiry committee had concluded that Borst and her ministry of Health did not react well to the health problems of survivors of the disaster. The motion was rejected by parliament after an eighteen-hour-long debate.
After a 2001 interview in the NRC Handelsblad Borst also faced another motion of no-confidence. In the interview she had said "It has been done" (Dutch: "Het is volbracht") on completing the law on euthanasia. Which according to the Bible are the last words of Jesus, on the cross. The orthodox Protestant parties ChristianUnion (ChristenUnie or CU) and Reformed Political Party (SGP), who had opposed euthanasia were insulted by this. Although the motion was not carried by parliament, Borst made her apologies for those words to parliament.
Before the 2002 elections she retired from political life. On 8 February 2003 she became honorary member of the Democrats 66. Borst held many positions in public life, serving as member of the Remembrance of the Dead and Liberation Day Committees. She also held many positions in the medical world, she was chairperson of the board of NIVEL (National Institute for Scientific Research in Medicine), chairperson of the Federation of Dutch Cancer Patients Organizations and chair of the advisory board of the Brain Foundation of the Netherlands.
Borst was found dead on the evening of 10 February 2014 in the garage at her home in Bilthoven by two close friends. The eighty-one-year-old former politician was reported to be in good health after recovering from breast cancer a few years before. Dutch police concluded that Borst died on 8 February, just hours after attending a party congress of the Democrats 66 in Amsterdam, where she was reported to be visibly active and upbeat and left the party congress on her own and walked to the Amsterdam Centraal railway station nearby. On 1 September 2015 the Public Prosecution Service released a statement that Borst died from forty-one stab wounds to her head, neck and hands. On 26 January 2015 police announced that a man with a criminal record had been arrested based on a DNA match; this man was already under arrest because he is suspected of murdering his sister. Early in 2016 he confessed to the murder of his sister (almost a year after the murder of Borst), and in February he confessed to having killed Borst because divine inspiration told him to do so, holding her responsible for the Dutch policy on euthanasia.