Meles, 57, was due to step down in 2015 at the end of his fourth term as prime minister. He died in a Brussels hospital last month suffering from an infecton after receiving treatment for an undisclosed ailment.
The Voice of America reported Ethiopian soldiers stood in formation as the flag-draped casket was carried into Meskel Square in Addis Ababa.
Many African leaders credited Meles for his dedication to development, the report said, but he was criticized in the West human rights abuses.
Meles' deputy Hailemariam Desalegn has taken Meles' powers, and was due to be sworn in after the funeral. VOA said he has pledged to continue his predecessor's policies.
The Times of India said at least 15 heads of state attended the funeral.