This is what we did.
First, your license has to be translated to English by an authorized translator.
Then this document should be legalized by the Ministry of Foreign Affairs in your country of origin.
From now on the process takes place in Ethiopia.
The document should also be legalized by your embassy in Ethiopia. (If you are still in your country of origin, it might also be possible to get the document legalized by the Ethiopian Embassy in that country, but haven't tried this option.)
Now go to the Foreign Affairs Bureau for Authentication of Documents, Oli Tower, northwest of Friendship Park (tall white building). They will check your documents and if they are OK, you should pay a registration fee at the bank in the entrance hall.
After this move on to your sub-city, Driver & Vehicle Licensing & Control Authority. Check with them what is needed in your case, if anything else than what I mention here.
They will tell you to go the Federal Documents Authentication Registration Agency in your
sub-city. To make it simple copy the complete document, exactly as it is. If there is text on both sides of the original, the copy should also have text on both sides. Also copy your Ethiopian ID card, both sides on one page. Then the copy will be checked against the original at the counter and after this you will have to pay a fee. You will get a receipt, bring this receipt to the Driver & Vehicle Licensing & Control Authority.
Bring the following with you there: Valid passport, valid driving license from your country of origin, Ethiopian ID card, one photo (will be scanned, you will get it back) + receipts from the Foreign Affairs Bureau and the Federal Documents Authentication Registration Agency. Please note that your blood group will be added on your driving license, check it out in case you are not sure. Your driving license will be issued immediately.