The WEU was formed by Belgium, Britain, France, Luxembourg and the Netherlands in 1948 and expanded to include Germany, Italy, Spain and others, but its role disappeared with NATO and the EU providing security in Europe.
"The WEU has therefore fulfilled its historic role. That is why we, the states party to the modified Treaty of Brussels, have collectively decided to end the treaty and thereby close the organisation," the statement said.
The 10 member states have requested the presidency to wind up the organisation's operations in their entirety by the end of June 2011.
In a separate statement, Belgian Foreign Minister Steven Vanackere said: "From a budgetary point of view, maintaining the WEU became difficult to defend."
Vanackere added that he hoped the defence dialogue carried out by the WEU would continue in some form or another.
A week ago, the head of the assembly Robert Walter said "the WEU as an organisation will be wound down within a year or so."
The WEU's founding principles were "to afford assistance to each other in resisting any policy of aggression", and "to promote unity and to encourage the progressive integration of Europe".
The very year after it was formed the eclipse of the western European body began with the formation of NATO, with the key inclusion of the United States.
But it became outdated as the Cold War ended, with the 27-nation European Union and NATO presiding over a largely peaceful Europe.
According to a European diplomat, British Foreign Secretary David Miliband wrote this month to the WEU's British delegation informing it of Britain's intention to renounce the body's founding treaty within the coming days.
Including associate and observer nations, the WEU is made up of 28 countries including most of the EU members along with Iceland, Norway and Turkey.
It currently has a budget of 13 million euros (17 million dollars) and a staff of 60.
The body's inter-parliamentary assembly is based in Paris while the official headquarters moved to Brussels a decade ago.
Walter said he expected official notification of the decision to wind the body down to be made by the end of the month.
The WEU's functions have been diminishing for years.
A decision was taken in 2000 to scrap ministerial meetings, since when all decisions have been taken by written procedure.
Britain, less attached to the idea of European integration than France, Spain and others, had remained more interested in the WEU due to its nature as an intergovernmental institution.
The last nail in its coffin was the passage in December of the EU's reforming Lisbon Treaty, which includes an assistance clause and permits the creation of ad hoc inter-parliamentary groups.
Nonetheless Walter said he hoped, with London's support, that the WEU could be succeeded by a "permanent conference" of representatives of national parliaments in Europe.