To meet the concerns, the initial funding will be voluntary and no cost targets for individual EU nations were announced.
Details of how the burden will be shared will be sorted out later by a working group.
Earlier EU leaders agreed a deal designed to secure the ratification of the Lisbon Treaty, which aims to streamline decision-making and bolster the bloc's role on the world stage.
Vaclav Klaus, president of the Czech Republic, the only country that had been holding out on ratification, said it would no longer raise objections.
Mr Brown, announcing the climate deal, said the EU discussions had been a success.
Oana Lungescu, BBC European affairs correspondent
"We can look the others in the eye," said the president of the European Commission, "we Europeans have done our job." But to critics, that job may look only half-done.
EU leaders have agreed that developing nations would need $150bn a year to tackle climate change and pledged they would pay their fair share. But they haven't said how much.
And poorer EU nations like Poland will continue on a voluntary basis or according to their means. It's now up to the other big global players - the US, China and India - to decide if that's enough for them to put an offer on the table and avoid failure in Copenhagen.
"We were aware that if we did not come together to make progress, the possibility of a deal [in Copenhagen] would be a lot less likely."
He said: "Europe is leading the way with these bold proposals - do not allow years to go by without action."
The EU said the amount to come from public funding from all countries to meet the estimated 100bn euros a year needed by 2020 would be between 22bn and 50bn euros a year.
However, it did not fix the EU's contribution, saying it would only pay its "fair share".
But Mr Brown did announce a "fast track" scheme to reduce carbon emissions, with the richest countries providing development finance to the poorest.
This would come in soon after the Copenhagen summit and would cost 5bn to 7bn euros immediately, to come from all richer countries.
He insisted that all these funding targets would be conditional on other richer countries making funding offers and on developing countries showing how they would spend the money.
European Commission President Jose Manuel Barroso said the agreement was "an important breakthrough that brings new momentum".
He said the EU nations had "agreed a negotiating mandate" for the Copenhagen climate talks.
"Next week, we'll meet the US president and will say 'let's make Copenhagen a success'," Mr Barroso said.
Fredrik Reinfeldt, PM of Sweden, which holds the rotating EU presidency, said: "The EU has a very strong negotiating position. This enables the EU to continue taking a lead in the negotiations and encourages others."
However, the Green bloc in the European parliament criticised the EU leaders for failing to fix the costing, calling the deal "a calamitous result for the climate".
"The EU preferred to give into dissension, opacity and internal tactics during the negotiations between the member states," the bloc's leaders said.
Gordon Brown: ''Europe is leading the way in making these bold proposals''
Joris den Blanken of environmental group Greenpeace, said: "[The EU] failed to use this opportunity to put its money where its mouth is.
"President Barack Obama should now step up and break the deadlock in negotiations."
International development charity ActionAid said the EU suggestion of 22bn to 50bn euros a year from public finance by 2020 was far below its estimate of 132bn euros a year.
Earlier, the Czech Republic was granted an opt-out from the EU's Charter of Fundamental Rights, similar to that of the UK and Poland, paving the way for the full ratification of the Lisbon Treaty.
President Klaus said he accepted this was a "significant exemption".
He added: "I am not going to raise any further conditions for the ratification of the Lisbon Treaty."
French President Nicolas Sarkozy said the treaty would "doubtless" come into force on 1 December.
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