Bemba and his family have visas to travel to Portugal, where he is to have treatment for a leg injury that was previously treated there, but Portugal had demanded written permission from the authorities for him to travel.
Portuguese diplomats have said Bemba is not moving into long-term exile in the country.
The United Nations peacekeeping force in Congo is expected to take Bemba to Kinshasa's N'Djili airport on Tuesday, possibly by helicopter.
Foreign diplomats have estimated that between 200 and 600 people were killed when fighting broke out on March 22 after Bemba's bodyguard defied a goverment order to disarm.
Bemba's several hundred fighters were beaten and he took refuge in the South African embassy.
Government officials initially said a warrant had been issued for his arrest for high treason, but said later such a warrant could not be issued unless the senate lifts the immunity he enjoys as a member.
The private radio and television stations owned by Bemba have not been allowed to broadcast since the clashes. The TV station, as well as his party headquarters, have been occupied by government troops and the homes of several of his political allies have been ransacked.
Bemba, who led a Uganda-backed rebellion against the government during the country's 1998-2003 war, lost a presidential run-off to Joseph Kabila last October.
The central African state's first free elections in more than 40 years had been intended to bring an end to years of chaos and violence but tensions between rival groups remain.