An estimated 615,000 Rohingya refugees have fled across the border into Bangladesh since August 25 when a new outbreak of violence began between the Myanmar military and armed militants in Rakhine state.
So far, no official details have been released on the agreement, what it would entail and under what circumstances the Rohingya would return.
A statement from Suu Kyi's spokesman confirmed the agreement had been signed but only said the pact was "a win-win situation for both countries."
Ro Nay San Lwin, a European-based Rohingya activist, told CNN that Bangladesh should not send any citizens back to Myanmar "unless citizenship and basic rights are guaranteed."
"I didn't find any clear statement how these refugees will be repatriated," he said. "I'm not sure whether they will be allowed to return to their original village. I'm not sure whether they will get back their own lands."
The Rohingya who have fled Rakhine state have brought with them stories of mass murder, rape and widespread destruction.
On Wednesday, US Secretary of State Rex Tillerson said Myanmar's actions against the Rohingya were clearly "ethnic cleansing."
Myanmar's military has repeatedly denied it has mistreated Rohingya civilians.
There is no indication how many displaced Rohingya might want to return to Myanmar in light of what has happened.
The agreement's announcement comes less than a week before Pope Francis is set to make a three-day visit to Myanmar. The Catholic leader is expected to push for greater acceptance of the country's Muslim minority.
It is also unclear how many refugees Myanmar might be willing to accept.
On November 15, Myanmar's commander in chief, Senior Gen. Min Aung Hlaing,
said preparations were being made to return refugees but "it is impossible to accept the number of persons proposed by Bangladesh.
"The situation must be acceptable for both local Rakhine ethnic people and Bengalis, and emphasis must be placed on (the) wish of local Rakhine ethnic people who are real Myanmar citizens," Hlaing wrote on his Facebook page.
"Only when local Rakhine ethnic people accept it, will all the people satisfy it."
Senior Myanmar authorities refuse to recognize the Rohingya as citizens
, saying they are Bangladeshi or Bengali.
UK-based Rohingya activist Jamila Hanan said it's essential all Rohingya be granted citizenship in Myanmar before they're repatriated, something the country has long denied them.
"(Otherwise it) would be a deal to send the victims of genocide back into the hands of their perpetrators, where they would almost certainly be locked up in concentration camps," she said.