It followed a campaign by The Guardian, which argued that the public had a right to know the contents of the letters sent between 2004 and 2005.
The office of the Attorney General vetoed a Freedom of Information request to have the letters published in 2012, but that was effectively overruled at the Supreme Court yesterday.
It had been argued that publishing the letters, which were nicknamed Charles' 'black spider memos' in reference to his handwriting, could undermine his neutrality. The episode also raised the question of the royal family exerting undue influence over the Government.
A Clarence House spokesperson said it was "disappointed the principle of privacy had not been upheld". David Cameron also called the ruling "disappointing", saying it was "fair enough" that Prince Charles was able to express his views to the government confidentially.
The Campaign for Freedom of Information director Maurice Frankel said: "This is a critical decision that strengthens the FOI Act. It says the courts not ministers normally have the last word. If the Government disagrees with a ruling on good grounds it should appeal.
"The veto is not a trump card to be slipped out of a minister’s sleeve to block any embarrassing disclosure. Ministers will now have to argue their case, not impose it."