Tens of thousands of Ethiopians waved the national flag, some openly weeping.
"He is our hero. All the progress in this city, and this country was because of his vision to make a better Ethiopia," said Amnet Melese, 24, a recent graduate from Addis Ababa University.
"He didn't care about anything apart from our country, it is so sad we have to say goodbye before he will see the results of his hard work".
Meles died aged 57 earlier this month in Brussels, where he had been receiving treatment for an illness still not clearly explained by the Ethiopian government.
Hailemariam Desalegn, Meles's deputy and now the country's acting prime minister, promised at yesterday's funeral to continue his predecessor's work with added vigour.
We affirm to the peoples of Ethiopia and to all our friends that we have renewed our covenant to pursue our goals and Prime Minister Meles' aims and ambitions with greater zeal and vigour," he told the crowd.
During a tour of Africa, Bill Clinton describes Meles as part of a “new generation” of African leaders devoted to democracy and economic reforms.