Speaking to the Huffington Post UK, Geldof praised Brand for his "articulacy and expressing the anger of the moment", after he sparked a controversy with an essay in the New Statesman magazine calling for the "overthrow of the current political system".
The Irish rockstar and political activist said: "We have to change and it needs to be in the context of how we live now rather than with some old-hat political ideal."
Geldof blamed the failure of capitalism on the banks going "out of control" and due to human greed, inventing "completely spurious" financial products.
"They ceased to [give money to others] and gave it to themselves through fraud, outright international global gangsterism.
In an impassioned attack on recent banking scandals, he went on: "That's what it was. Mispricing of products, fraud. Mis-selling of products, fraud. Fixing the interbank lending rate. Fraud. It was fraud on an unprecedented scale! They sucked billions out of the world economy, destroying individuals, companies and countries."
"Russell [Brand] is completely right. That model cannot sustain us as we saw, it bankrupted Greece, almost Italy, almost France and almost Ireland. It just can't work."
Geldof spoke to HuffPostUK after talking to young entrepreneurs at an event hosted by the Rockstar Group, a mentoring organisation.
The musician spoke at the event about his entrepreneurial journey, drawing on his time with the Boomtown Rats, founding the Band Aid charity super-group and starting up the Live 8 and Live Aid concerts.
Geldof warned Brand that replacing the current political system with anarchy was "not viable or plausible", adding: "You can't just have a free for all. It just wont work because we will form structural organisations within that as it's the kind of thing we do."
However, he said the bankers' immense levels of pay posed a serious threat to society. "When you have these supposed masters of the universe averaging more than 248 times the average worker's pay, you have a serious problem of inequality. Inequality stops a society functioning and so it has to stop.
"I do think the version of democracy that we have been living with just may not be viable for very much longer. We will have something where we have proper freedom and elected representation."
"We all co-operate in the knowing lie, which is that everybody promises more and that the economy will inevitably grow. what does that mean? It means more, more of what? That's not viable in an unsustainable and finite world.
"Nor can you in a four year electoral cycle put into place programmes that would help to ameliorate the effects of that. If the economy is affected in that way by definition politics are so that the politics that we've grown up with in a different economy cannot work in a new one, there has to be a newer type of politics.
"You will see a change in the type of politics. It'll still be our government, it needs to be otherwise you'll have problems and it still needs to be a more coherent economy."