HSBC will repay £8mln to 115,000 customers, while Santander has yet to quantify how many of its customers were affected.
Competition watchdog the CMA said that HSBC had twice breached rule 6 of the Retail Banking Market Investigation Order, while Santander had racked up six contraventions.
The Spanish-owned bank has agreed to refund customers affected by the breaches, which occurred from the introduction of the new rules in February 2018.
Both banks have also been told to instigate an independent review of their compliance with Part 6 requirements up until the end of this year.
Holders of HSBC’s Everyday Account and Advance Bank Account are charged £5 a day if they go into an unarranged overdraft up to £80 monthly.
Santander charges £6 per day for unauthorised overdrafts on its Everyday Current Account.
In May, the bank paid back £1.4mln after failing to text 20,000 account holders that they were going into the red.