Barreto, a former Ghana coach and assistant manager of Dynamo Moscow, was given the job after the EFF failed to reach an agreement with first choice Goran Stevanovic of Serbia.
"(Barreto) fits well in our plans. He has experience at all levels," EFF chief Junedin Beshah told Reuters.
The 57-year old Barreto signed a two-year deal on Tuesday on a salary of $18,000 a month.
"Our primary aim now is to qualify for Morocco," Junedin said, referring to next year's African Cup of Nations. "We need to better our previous record."
Ethiopia - nicknamed the 'Walyas' after an antelope endemic to the Horn of Africa country - were previously managed by Sewnet Bishaw, who was sacked in February after a dismal run at this year's African Nations Championship (CHAN).
Under Sewnet, however, the Walyas last year qualified for the African Cup of Nations for the first time in three decades.
They also reached the final knockout round for a place at this year's World Cup in Brazil in what would have been east Africa's first-ever spot at the finals but they lost over two legs against regional heavyweights Nigeria.
The draw for the African Cup of Nations qualifiers will take place this month with Ethiopia among 21 countries with a bye to the group stages.
The Walyas won their maiden African Cup of Nations in 1962 but have not lifted the trophy since.
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- African Cup of Nations