This legislation was first outlined by the Chancellor Alistair Darling in July.
Under the terms of the act, the UK financial watchdog - the Financial Services Authority (FSA) - would be given the right to intervene to stop banks taking too many risks.
The act would "ban the old bonus systems and make it impossible for firms to go back to using them," Mr Brown said.
Companies that did not comply with the new measures would have penalties imposed on them, he added.
Speculators and short term deals would no longer be rewarded so highly, he said.
The prime minister argued that the measures were necessary because there was already evidence that banks wanted to return to paying big bonuses that encouraged the excessive short-term risk taking that contributed to the financial crisis.
Excessive bonuses have caused public outrage in the US and in Europe, particularly at banks that have received state aid during the financial crisis.
But despite the backlash against what many see as excessive pay, a number of top banks have already been setting aside huge sums of money to pay in bonuses.
The comments come after US President Barack Obama hailed "tough new regulations" for global financial institutions after the G20 summit in Pittsburgh on Friday.
The group of leading economies agreed that bonuses should no longer be guaranteed for many years, and that a part of them should be deferred to encourage longer-term investment strategies.
They also agreed that bonus payments could be clawed back if a bank makes a loss, and that they should not exceed a certain percentage of a bank's revenue.
But there was no agreement that bonuses should be capped, as some leading nations had been calling for.
The only leading economy to go this far is the Netherlands.
The G20 also agreed to take action on the capital reserves that banks need to hold.
It said it would come up new rules on reserves by the end of next year.
If banks had held more money in reserve, they would not have got into such trouble when the loans that they made could not be repaid.
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.