Momock Bambang Samiarso said they will be taken from Kerobokan jail on Wednesday and flown to Nusakambangan, the central Java island Indonesia has reserved for the executions.
He later told reporters the move could happen even earlier on Wednesday. "Just stand by from the morning," he said.
The pair will get 72 hours' notice of their executions.
Kerobokan prison's governor says Chan and Sukumaran are aware of the development and have been giving things to other inmates.
The news has dismayed the mens' lawyers, who hadn't been officially informed as of Tuesday afternoon.
Todung Mulya Lubis said they had just lodged an appeal in a Jakarta administrative court that would ordinarily give his clients the right to a two-week schedule of hearings.
In addition, the judicial commission had requested statements from Chan and Sukumaran in relation to a complaint about bribery in their first trial.
With all this going on, Mr Lubis says, it is difficult to argue their legal avenues have been exhausted.
"This is a process that cannot be ignored by anyone, including the attorney-general," he told reporters in Jakarta.
"When you talk about the life of a human being ... they should be given every opportunity available under the law."
Attorney-General HM Prasetyo argued presidential clemency was the last stop in the legal process, and it has been denied to the men.
President Joko Widodo did not give reasons for the rejection, but has vowed to send all death row drug offenders to the firing squad as part of his anti-drugs policy.
Along with Chan and Sukumaran, seven other foreigners and one Indonesian will be executed. Several of the foreign governments, including Australia, have pleaded for Mr Joko's mercy, but he says his country's stance is clear, and its laws won't be interfered with by outsiders.
Chan's brother Michael and Sukumaran's mother Raji visited them in prison on Tuesday, but left before news of the transfer was announced.
It's unclear if they will be able to see the men again before they leave Bali, or when they are on Nusakambangan, where they will be put in isolation cells before their executions.
Indonesia has not set a date for the executions, with authorities expected to do that once all 10 prisoners are on the island.
-AAP