They were identified as Sisom, Moro Mohammad, Morrison and Anthony, hailed from Naigeria and Ghana.
Four laptops, some SIM cards, and six mobile handsets were recovered from their possession.
Although a team of the CID team arrested them on Tuesday, the information was disclosed through a press briefing on Wednesday.
Addressing the briefing, Special Superintendent of Police of CID Syeda Jannat Ara Begum said they arrested the four on the basis of a complaint by victim Khairul Islam.
The fraudsters initially make friendship with opposite gender people on facebook and start mutual conversation.
At one stage, they offer a so-called gift box, containing valuable items worth millions of dollars, to the victim and ask to receive the parcel from a customs office. They complete the entire conversation using a fake messenger ID, revealed SYeda Jannat.
When the victim reached the designated customs office, one of the fraudsters identified himself as customs commissioner and asked the victim to receive the parcel by paying a large amount of money through several bank accounts.
He pressurized the victim and even intimidated him saying that failure to receive the parcel can lead to different legal complications.
To avoid any unwanted odd, the victim deposited TK 55,000 in several bank accounts provided by the so- called customs officer.
This is how the fraudsters swindled crores of taka from a number of people in the last few months, she added.
Syeda Jannat Ara also revealed that the four foreigners have been staying in Bangladesh and deceiving people for a long time.
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They even failed to show any valid passport or document that could allow them to stay here, she sadded.
They initially enter Bangladesh using tourist, player, business and student visas.
Then got engaged in such fraudulent activities with the help of some local agents.
She said the CID continued its investigation to obtain detailed information about the bank accounts. Besides, the department is working to bring the local collaborators under law, she added.
Victim Khairul Islam filed a case with Kafrul Police Station in this regard.