Cluster bombs have been used in countries including Cambodia, Kosovo, Afghanistan and Lebanon.
They are made up of a big container which opens in mid-air, dropping hundreds of smaller individual sub-munitions, or "bomblets", across a wide area.
Countries like the US, India, Pakistan and Israel claim such munitions are highly useful on the battlefield, but opponents say that where the bomblets fail to explode they leave a deadly legacy for civilians.
A father relives the day his five-year-old son was killed by a cluster bomb
During the conference, delegates have heard first-hand accounts from survivors of cluster bomb attacks.
Speaking at Downing Street earlier, Mr Brown said: "I am delighted that the negotiations in Dublin have come to a successful conclusion and congratulate the Irish Government and all those involved.
"I am confident that this agreement is in line with British interests and values, and makes the world a safer place."
The BBC's Paul Adams said he understood the agreement would outlaw the two types of cluster munitions currently held by UK forces, but would not prevent countries from developing future generations of weapons based on the concept of sub-munitions.
And he said it appeared the UK hoped other countries not present in Dublin, notably the US, might be persuaded to accept the treaty later.
Using British soil
One stumbling block for the treaty could be the stockpile of cluster munitions the US military keeps at bases on British soil.
It will be very difficult for the US to engage in operations with countries who have banned this weapon and continue to use them
Simon Conway Cluster Munitions Coalition
The British representative in Dublin, John Duncan, said the UK would work with Washington to find a solution to the issue.
But in a statement, the Pentagon stood firm, saying: "While the United States shares the humanitarian concerns of those in Dublin, cluster munitions have demonstrated military utility, and their elimination from US stockpiles would put the lives of our soldiers and those of our coalition partners at risk."
Some campaigners do believe countries like the US will change, however. They cite the landmine treaty of 1997 that was never signed by the US, Israel, Russia or China, yet those nations have not used landmines since it came into effect.
Simon Conway, from the Cluster Munitions Coalition, said there would now be "massive" pressure on the US.
"We think now that all of America's key allies have just renounced the weapon it will be very difficult for the US to engage in operations with countries who have banned this weapon and continue to use them," he said.
Liberal Democrat foreign affairs spokesman Ed Davey said the prime minister must make clear whether he would continue to allow the US to store its own cluster munitions on British territory.
"If he is serious about ending the scourge of these weapons, he must bring this abuse of the 'special relationship' to an end," Mr Davey said.
HOW A CLUSTER BOMB WORKS
1. The cluster bomb, in this case a CBU-87, is dropped from a plane and can fly about nine miles before releasing its load of about 200 bomblets. 2. The canister starts to spin and opens at an altitude between 1,000m and 100m, spraying the bomblets across a wide area. 3. Each bomblet is the size of a soft drink can and contains hundreds of metal pieces. When it explodes, it can cause deadly injuries up to 25m away.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.