The mobile phone giant promised to make it up to customers "the O2 way" after many UK users of its network were left without mobile data, texts and calls for part of last Wednesday and Thursday.
Despite only some customers being affected by the problems, O2 has decided to offer compensation to all its users.
On its Twitter page, the firm said today: "We're #sorry for last week. Equivalent of 3 days back for those directly affected & a £10 O2 voucher for everyone on O2."
In a blog post, the firm added: "As we said in our last update, we want to make it up to our customers for the loss of service some people experienced last week.
"The issue we had was unprecedented and we recognise that this caused inconvenience and frustration to those impacted over that one-day period."
O2 said that it has identified all the customers directly affected - their device could not connect to the O2 network - and these people will now be offered the equivalent of three days back for the disruption as "a gesture of goodwill and to say sorry".
Pay monthly customers will receive 10% off their July subscription, which will be applied to their September bill.
Pay-as-you-go customers will get 10% extra on their first top up in September, added automatically.
Available to download anytime from September 1 to 30, the voucher can be redeemed via the O2 Priority Moments app or online via www.o2.co.uk/priority.
There is no minimum spend for the voucher, but only one can be used per transaction and no change will be given.
"We will contact all O2 consumer customers and those small businesses with fewer than 10 connections by the end of the day on July 27 giving full details. This will be by text message," said O2.
"Other business customers will receive communications through their account managers or our channel partners in the coming days giving full details."
O2's problems started at 1.30pm on Wednesday (July 11) when a fault occurred with one of its network systems, resulting in some mobile phone numbers being unable to register correctly with the network.
The firm said that it deployed engineers "as soon as possible" to work on the issues, but it was not until 8am on Thursday morning that the 2G voice network was restored for affected customers.
O2 was able to restore 3G mobile data access later in the day, although some users were still experiencing problems right into the evening, meaning the partial blackout lasted more than 24 hours.
After services were completely restored on Thursday, O2 Telefónica UK chief executive Ronan Dunne said that he was "very sorry" for the problems, and stressed that he would focus on restoring customers' "confidence and trust in O2".