The telecoms regulator imposed the fine after concluding EE made "fundamental billing mistakes" which resulted in £250,000 in extra charges.
Ofcom’s probe found EE broke a fundamental billing rule on two separate occasions related to the use of its customer services helpline.
EE customers who used the 150 customer service number while roaming within the European Union were incorrectly charged as if they had called the US, with 32,145 customers overcharged to the tune of about £245,700.
While Ofcom accepted EE did not set out to make money from the billing mistakes, the watchdog criticised EE for "carelessness or negligence".
Ofcom said: "EE wrongly decided it couldn’t identify the people it overcharged and was proposing to give their money to charity, which would have left them out of pocket."
Then, despite making it free to call or text the 150 number from within the EU from 18 November 2015, EE continued to bill 7,764 customers up until 11 January 2016, Ofcom said. This led to customers being overcharged by £2,203.33, although EE did promptly issue full refunds.
While the majority of customers have now been refunded, Ofcom said EE was unable to identify at least 6,905 customers, who were more than £60,000 out of pocket in total.
EE has made a donation of just under £62,000 to charity in lieu of the payments owed to these customers. But, in addition to today’s fine, Ofcom is requiring EE to make further attempts to trace and refund every customer who was overcharged.
Lindsey Fussell, Ofcom’s consumer group director, said: "EE didn’t take enough care to ensure that its customers were billed accurately. This ended up costing customers thousands of pounds, which is completely unacceptable.
"We monitor how phone companies bill their customers, and will not tolerate careless mistakes. Any company that breaks Ofcom’s rules should expect similar consequences."
Last year, Ofcom fined Vodafone £4.6m for mis-selling and not handling complaints properly.