The new rules will affect anyone taking money out of a personal pension from 1 April 2017.
The Financial Conduct Authority (FCA) said providers who already charge less than 1% will not be allowed to raise their fees.
Those taking out new pension contracts will face no early exit charge at all.
Workplace pensions will be subject to the same rules, but these will not come into effect until October 2017, the Department for Work and Pensions (DWP) announced.
Christopher Woolard, executive director of strategy and competition at the FCA, said: "People eligible for the government's pension reforms should feel able to access them as they wish.
"The 1% cap on early exit charges for existing pensions, and the 0% cap for new contracts, will mean that current and future savers will not be deterred by these charges from accessing their pension pots."
Previously some pension providers were charging fees of up to 10%, after the government announced that anyone over the age of 55 could withdraw as much as they wanted from their pensions, subject to income tax.
The "pension freedoms" came into effect in April 2015.
However, some experts believe the 1% cap is still not low enough.
"The cap on early exit fees for pensions, including occupational schemes, is a start, but 1% of a Â£100,000 pension is still a Â£1,000 charge for accessing your own savings," said Tom Selby, senior analyst at investment platform AJ Bell.
"We hope the authorities continue to monitor the cap, to assess whether it should be lower or even abolished if early exit penalties continue to prevent people utilising the new flexible pension rules."
Early exit charges for people taking money out of their pension pots will be capped at 1%, the financial regulator has confirmed.