The mobile operator said it has identified the customers who were unable to register correctly on its network last Wednesday, when a system fault caused an outage. A third of O2's 23 million customers were affected.
In a statement, the company said: "We are giving them 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 subscriptions, which will be applied to their September bill.
Pay & Go customers will receive 10% extra on their first top-up in September.
In addition, all O2 customers will be thanked for their support with a £10 O2 voucher to spend in store, which can be redeemed via the O2 Priority Moments app or online at www.o2.co.uk/priority.
It will be available between 1 and 30 September to download through Priority Moments and redeem in store, with no minimum spend, one voucher per transaction and no change given.
Consumer and small business customers will receive a text from O2 between now and the end of Friday 27 July consisting of an apology and personal confirmation of what it is doing to redress the situation.
Business customers with over 10 connections will receive communications through their account managers or O2's channel partners giving full details.Follow @DanFareyJones