The Information Tribunal upheld a decision by the Information Commissioner that details of the sessions on 13 and 17 March 2003 should be disclosed.
The meetings considered the highly controversial issue of whether the invasion was allowed under international law.
In its ruling, the Tribunal said: "We have decided that the public interest in maintaining the confidentiality of the formal minutes of two Cabinet meetings at which ministers decided to commit forces to military action in Iraq did not... outweigh the public interest in disclosure."
The arguments in favour of keeping the formulation of Government policy secret and preserving the principle of collective responsibility were defeated in this "exceptional case", the ruling said.
The Tribunal said its decision had been "difficult" and carried by a majority rather than unanimously.
The ruling opens up the prospect of one of the most controversial Government decisions of recent years being laid bare - although the Tribunal stressed that disclosure would not necessarily set a precedent.
The Tribunal said: "The decision to commit the nation's armed forces to the invasion of another country is momentous in its own right, and ... its seriousness is increased by the criticisms that have been made (particularly in the Butler Report) of the general decision-making processes in the Cabinet at the time.
"There has also been criticism of the Attorney General's legal advice and of the particular way in which the March 17 opinion was made available to the Cabinet only at the last moment and the March 7 opinion was not disclosed to it at all."
Information Commissioner Richard Thomas said: "I am pleased that the Tribunal has upheld my decision that the public interest in disclosing the official Cabinet minutes in this particular case outweighs the public interest in withholding the information.
"Disclosing the minutes will allow the public to more fully understand this particular decision."
The Cabinet Office now has 28 days to decide whether to appeal to the High Court against the ruling.
Downing Street said: "The Information Commissioner has just made an announcement on this and we are considering our response."
The Tribunal said: "The approach adopted during the Cabinet meetings by those who were aware of the March 7 opinion, as well as those who were not, is of crucial significance to an understanding of a hugely important step in the nation's recent history and the accountability of those who caused it to be taken."
The public interest in favour of disclosure had not been "significantly reduced" by the fact that inquiries had already been carried out into the invasion.
"In the view of the majority the questions and concerns that remain about the quite exceptional circumstances of the two relevant meetings create a very strong case in favour of the formal records being disclosed," the ruling stated.
The majority of the three-man panel concluded that the public should be allowed to "make up its own mind" on the discussions.
The "very unusual" nature of the situation "reduced the risk" that releasing the details would set a precedent.
While it accepted the case for releasing formal minutes taken by civil servants, the Tribunal said informal minutes would not "contribute materially to public knowledge or understanding".
There will also be redactions from the minutes to protect the UK's international relations.
Shadow foreign secretary William Hague said: "Rather than have items of evidence dragged into the public domain piece by piece the Government should set up a fullscale Privy Council inquiry into the origins and conduct of the Iraq war.
"The sooner we can learn the lessons of the war the sooner we can apply them. It is imperative to begin an inquiry before memories have faded, emails have been deleted and documents have disappeared."
That did not mean minutes should only be made public in "extreme circumstances", but each case would have to be considered on its merits, the ruling added.
Liberal Democrat MP Sir Menzies Campbell said: "This is a major step forward in explaining the supine attitude of members of the Cabinet towards military action and is clearly in the public interest.
"The Government only have themselves to blame for this. By procrastinating over an inquiry into the political events before the Iraq war they have left themselves wide open."
Former Cabinet minister Clare Short, who resigned over Britain's involvement in Iraq, said today: "I think people will be disappointed about how little the minutes will say.
"For example, they never attribute different points to different people. They are always in very generalised terms.
"So I think it's very interesting indeed that the Information Commissioner has said they must be revealed, but I think they will disappoint people."
Ms Short said there was "very little proper discussion" in the Cabinet, adding: "Cabinet meetings were limited and the minutes are very generalised and limited."
Asked why the Government did not want the public to see the minutes, she said: "One, it will be revealed what a weak instrument the Cabinet was.
"But secondly, will it go further? For example, there are two civil servants, one for home affairs and one for foreign affairs, who take a complete note of everything that's said.
"Would the courts go on to demand that that was revealed? Or the Cabinet Secretary ... takes a full, very complete manuscript note himself.
"Now if those came out, we would really be getting towards a record of what was said."
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