The AFP news agency reports that the United States, Ireland and Britain have called for an emergency UN Security Council public meeting over the conflict-hit northern Tigray region.
Residents told the BBC that the forces had taken control of the streets and the airport. They also said they saw the Ethiopian military leaving the city during the day.
The Ethiopian government has not confirmed the loss of Mekelle but has declared a unilateral ceasefire.
The UN Secretary-General Antonio Guterres said he had spoken to the Ethiopian prime minister, Abiy Ahmed, and was hopeful that a cessation of hostilities would take place.