In July, the FCA estimated that the effect of the price cap would be that 11% of current borrowers would no longer have access to payday loans after 2 January 2015.
The move was welcomed by debt charities and consumer groups.
Which? executive director Richard Lloyd said: “Today the regulator offers hope for millions of borrowers stuck in a cycle of debt, by confirming their plans to rein in the cost of payday loans and crackdown on excessive default charges.
“In the meantime the FCA must keep the cap on the cost under review and tightened up further if it doesn’t work as intended.”
Joanna Elson, chief executive of the Money Advice Trust, the charity that runs National Debtline, said: “We hope that these measures will bring an end to the inappropriate lending that we have seen from this industry.
"However, the FCA will need to be vigilant to ensure that lenders do not simply change their business models to try to evade the rules.
"Calls to National Debtline about payday loans have actually declined slightly from their peak in 2013, but we are still seeing around one in 10 calls relating to this kind of borrowing."
