One base for the unmanned aircraft is being established in Ethiopia and another base has been installed in the Seychelles in the Indian Ocean, the newspaper reported.
A small fleet of "hunter-killer" drones resumed operations in the islands this month after an experimental mission demonstrated that the unmanned drones could effectively patrol Somalia from there, the report said.
The US military also has flown drones over Somalia and Yemen from bases in the African nation of Djibouti and the CIA is building a secret airstrip in the Arabian Peninsula to deploy drones over Yemen, the article said.
The White House declined comment on the report.
The US and Seychellois officials have previously acknowledged the drones' presence in the island but have said that their primary mission was to track pirates.
However, classified US diplomatic cables show that the unmanned aircraft have also conducted counterterrorism missions over Somalia, about 800 miles (1,287 km) to the northwest, the Post reported.
The newspaper said the cables, obtained by the anti-secrecy group WikiLeaks, reveal that US officials asked leaders in the Seychelles to keep the counter-terrorism missions secret.
Source: Reuters; The Washington Post