Minzayar Oo and Hkun Lat were picked up from the Cox Bazar's region in early September because they were working as journalists on tourist visas, police said.
They were released on bail after calls from Germany's GEO magazine, which had assigned Minzayar Oo to cover the influx of Rohingya refugees from Myanmar, as well as rights groups.
On Tuesday, the pair were headed back to Myanmar while the case against them was being dropped, their lawyer Jyotirmoy Barua said.
"Finally, they are going back to their country," he said.
GEO magazine said Minzayar had travelled to Bangladesh on Sept. 6, and was detained the next day.
Some 582,000 refugees from Myanmar have poured into Bangladesh since Aug 25, when attacks by Rohingya militants on security posts triggered a Myanmar army crackdown in response.