The 52-year-old was taken to a police station about a week ago after repeatedly being caught at the wheel while over the legal alcohol limit, they said.
The man, who had no previous criminal record, then surprised officers by telling them he had stabbed to death a 38-year-old woman in November 1991 in Bonn, North Rhine-Westphalia state.
He told police that as a 26-year-old student, having long had "violent and homicidal fantasies", he had rung the woman's doorbell, entered her home, handcuffed her and, when she screamed, repeatedly stabbed her.
Police and prosecutors, after reopening the file on the long unsolved murder, believe details the man gave in his confession suggest he is telling the truth.
Investigators are also checking whether the man, who now lives in Lower Saxony state, may have committed other crimes.
The man himself had seemed not entirely clear on why he had spontaneously confessed to the killing, police said.
He had merely told police that he had lost hope as the drink-driving offences would cost him his job.