The former Ghana coach will be unveiled on Tuesday according to EFF president Juinedi Basha.
“We’ve selected Barreto to be the new coach, we’ve agreed on the terms and conditions,” Basha told BBC Sport.
He replaces Sewnet Bishaw, who was sacked in February after a poor campaign at the African Nations Championship in South Africa.
Barreto’s main task will will be to lead the Walya Antelopes to the 2015 Africa Cup of Nations in Morocco.
Ethiopia are one of 21 nations who have gone straight into the group stages of the Nations Cup qualifiers, which get underway in September.
The 57-year-old quit Ghana in September 2004 after just nine months in charge, citing problems in communications with the country’s football association.
He went onto coach Portuguese side Maritimo and several other clubs in Europe including Russian sides Dynamo Moscow and Kuban Krasnador.