The ISNA news agency, in a report published in the "Donya-E-Eqtesad" daily, quotes Hassan Shariati, the judiciary chief of northeastern Khorasan-e Razavi Province, as saying the two people -- who are unidentified -- were repeat offenders.
They had previously been convicted of drinking alcohol twice and lashed 80 times each.
Shariati said the death penalty for the third conviction had been upheld by Iran's Supreme Court.
"We will not show mercy in alcoholic beverage offenses," he said, "and we will sentence the offenders to the harshest letter of the law.”
Executions for violations of Iran's alcohol laws are believed to be rare, however.
Iran's "Shargh" daily reports that the last time an execution was ordered for a repeat offender of the country's alcohol laws, in 2007, the sentence was overturned after the convict expressed contrition.
Since the 1979 Islamic Revolution, under Shari'a law, alcohol consumption has been strictly forbidden in Iran. That hasn't stopped the smuggling of a reported 60 million to 80 million liters of alcohol into the country each year, however.
Alcohol is readily available on the black market, despite the severe penalties.
Iran's police chief, Esmail Ahmadi Moghadam, is quoted as saying that Iran has some 200,000 alcoholics.
Only members of Iran's Christian minorities are exempt from alcohol laws, but they are required to drink behind closed doors.
As RFE/RL's Golnaz Esfandiari and Mohammad Zarghami reported last week, consumption of alcohol is on the rise in Iran, with the amount of confiscated alcohol increasing by 69 percent in the past year:
"Alcoholic drinks are just one type of tranquilizer," he says. "We live in a society where there is economic pressure, social problems, and high inflation. People escape with alcohol to alleviate the pain.”
The head of the Health Ministry's Policy Making Council, Bagher Larijani, warned last month about "worrying" reports from hospitals and physicians over high alcohol consumption in southern districts of Tehran where poorer families reside.
Other crimes punishable by death in Iran are murder, rape, armed robbery, and drugs trafficking.
According to Amnesty International, Iran executed at least 360 people in 2011, most of them for drug-related offenses.