Rooney, whose arrest in Cheshire on September 1 has led to his personal life coming under scrutiny, will now serve a two-year driving ban and perform 100 hours of unpaid work as part of a 12-month community order.
In a statement released after the hearing, the Three Lions' all-time leading scorer said: "Following today's court hearing I want publicly to apologise for my unforgivable lack of judgement in driving while over the legal limit. It was completely wrong.
"I have already said sorry to my family, my manager and chairman and everyone at Everton FC. Now I want to apologise to all the fans and everyone else who has followed and supported me throughout my career.
"Of course I accept the sentence of the court and hope that I can make some amends through my community service."
Rooney's lawyer added that the striker "wishes to express his genuine remorse for...a terrible mistake".
The 31-year-old, also ordered to pay £170 when he appeared at Stockport Magistrates' Court, featured for 82 minutes in Everton's 4-0 defeat to former club Manchester United on Sunday afternoon.