The banks will replace a £25 set up fee that customers are currently charged for going over their agreed limit with a £5-a-day "usage fee", capped at a maximum of £80 for one monthly charging period.
Customers do not get charged by more than they go over their authorised overdraft limit by, so for example if they only dip into an unauthorised overdraft by £15, this is the maximum that they will be charged for doing so, even if the customer remains over this limit for more than three days. They also have a £10 unauthorised overdraft "buffer", before any charges start to kick in.
HSBC and First Direct said they will also alert customers who go over their pre-arranged limit by text and they will not be charged if their balance is back within the limit before 11.45pm on the same day.
The banks said there will continue to be no changes for customers who stay within their agreed overdraft limit and they will continue to pay interest as before.
"These changes have been designed to provide a simpler way for customers to understand the cost of any borrowing not agreed in advance."
Andrew Hagger, founder of Moneycomms.co.uk, said: "It's good to see that the daily charge and maximum monthly charge have both been significantly reduced.
"I'm also pleased to see that unlike some of its rivals HSBC hasn't shifted the cost burden for unauthorised borrowing by increasing the costs for agreed overdrafts.
"The decision to opt in all customers to the text alert system to warn of potential unauthorised overdrafts is much better than offering a voluntary opt in service - this strategy should help keep the number of people charged a £5 daily fee much lower.
"To avoid being hit with unauthorised overdraft charges, customers should be encouraged to arrange an authorised overdraft limit with their bank, even if they don't think they're going to use it."