Bangladesh's Foreign Minister Abul Hassan Mahmood Ali said that during his recent talks with a senior Myanmar representative, a consensus on the issue had finally been achieved.
"The talks were held in a friendly atmosphere, and Myanmar has made a proposal to take back the Rohingya refugees," Mahmood Ali was quoted by Al Jazeera as saying.
Reuters, in turn, cited Myanmar' Minister of Social Welfare, Relief and Resettlement Win Myat Aye as saying that bringing back the Rohingya refugees who have fled to Bangladesh remains Myanmar's "immediate priority."
"The repatriation process can start any time for those who wish to return to Myanmar. The verification of refugees will be based on the 1993 agreement between the Myanmar and Bangladesh governments," Aye said.
Myanmar does not recognize the Rohingya Muslims as citizens. Instead, they are largely seen as illegal immigrants from Muslim Bangladesh.
The attacks were followed by a brutal state crackdown, which resulted in clashes and the death of hundreds of Rohingya people.
More than half a million Rohingya Muslims fled their nation's army as it advanced, crossing into neighboring Bangladesh.