The banker, known as Mr Y, was unresponsive after his heart attack past year and there was no chance of recovery.
It comes after a legal ruling about a man in a vegetative state, who was unlikely to ever regain consciousness.
He had not left any instructions about wanting to refuse treatment, but his family said he would not want to be kept alive given his poor prognosis.
The decision will make it easier to withdraw food and liquid to people in long-term vegetative states, allowing them to die.
Lady Black acknowledged that there could be occasional cases in which circumstances would make an application required or desirable, but said that generally decisions such as those involving Mr Y should be made without court input.
When families and doctors agree it's in the best interests of the patient, medical staff will be able to remove feeding tubes without applying to the Court of Protection.
Tom Lax, a senior solicitor at Bolt Burdon Kemp, said the judgement, which mentions the costs to the health service of court cases, threatened to reduce legal and moral concerns to political ones.
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The judge agreed, but the official solicitor appealed on behalf of Mr Y - an appeal which has now been dismissed.
It is estimated about 24,000 people in the United Kingdom are in a persistent vegetative state or a minimally conscious state.
Mr. Y died before the case was heard by the Supreme Court, but the case proceeded because of the importance of the issues raised. It is about who decides that question'.
A police man stands outside the Supreme Court before the decision of a court ruling on whether Theresa May's government requires parliamentary approval to start the process of leaving the European Union, in Parliament Square, central London, Britain, January 24, 2017.
Lady Black ruled there was no violation under the Human Rights Convention. He has since died, but the case continued in order to establish the law.
'If the provisions of the MCA 2005 (Mental Capacity Act) are followed and the relevant guidance observed, and if there is agreement upon what is in the best interests of the patient, the patient may be treated in accordance with that agreement without application to the court'.