"Those refugees from Bangladesh who meet four key criteria will be allowed to come back," the official said, adding that Myanmar expected around 2,500 refugees would meet the conditions, which include legally proving citizenship.
Ethnic Rohingyas will not be included in the repatriation as they are not Myanmar citizens but Bangalees who migrated around the time of the Second World War when both countries were under British rule, he added.
Described by the United Nations as one of the most persecuted minorities on earth, the Rohingya have no legal right to own land in Myanmar and are banned from marrying or travelling without permission.
Every year, thousands of Rohingya stream across the border into Muslim-majority Bangladesh from Myanmar's northern Rakhine state.
Bangladesh, which views the Rohingya as economic migrants and has repeatedly called on Myanmar to take them back, said the latest refugee deal "was nothing new", Dhaka's foreign secretary Mijarul Quayes said.
Some 28,000 Rohingya are recognised as registered refugees and live and receive aid at an official UN camp in Bangladesh. This figure is a fraction of the 200,000 to 300,000 unofficial refugees, according to government estimates.
UNHCR has not been officially informed of any repatriation of refugees but is seeking clarification on any new deals from both governments, Jing Song, UNHCR external officer in Bangladesh said.
"Our official stance is that repatriation has to be voluntary," she added.
Mojibar Rahman, a registered Rohingya refugee who works as a teacher in one of the UN camps in Bangladesh said most Rohingya did not want to return to Myanmar.
"We thought that after the election the situation would improve for Rohingya in Myanmar, but it hasn't. Now, we are hearing we'll be forced to return -- but no one wants to go back," he said.