His employer, English-language news site Frontier Myanmar, said he was on a flight out of Myanmar.
The military spokesperson Major-General ZAW TUN confirmed to the BBC that he would be allowed to leave the country.
Fenster, who was Frontier’s managing editor, was detained in May as he was about to fly back to the US.
He is one of dozens of journalists, and thousands of people overall, to be held since a military coup in February.
