A government spokesman said 57-year-old Mr Meles had been ill for a year and had been recuperating before being suddenly rushed to intensive care.
The secretive country would give no information as to the cause of his death.
Mr Meles seized power from a military junta in 1991 and was credited for steering one of the world's poorest countries to high economic growth.
Rights groups criticised him for cracking down on dissent, with one opposition website describing him as a "genocidal tyrant".
However, the West generally turned a blind eye to repression, reluctant to pick a fight with a partner in the fight against al Qaeda-linked groups in Africa.
UK Prime Minister David Cameron hailed Mr Meles as an "inspirational spokesman for Africa".
He said: "His personal contribution to Ethiopia's development, in particular by lifting millions of Ethiopians out of poverty, has set an example for the region."
The European Commission said Mr Meles had worked hard on African unity, climate change and development, but hoped the country would improve its human rights record.
European Commission President Jose Manuel Barroso said: "I hope Ethiopia will enhance its path of democratisation, upholding of human rights and prosperity for its people, and of further regional stabilisation and integration."
Deputy Prime Minister Hailemariam Desalegn will be sworn in as acting Prime Minister until a successor is chosen.
Negasso Gidada, a former President during Mr Meles's tenure and now chairman of the opposition Unity for Democracy and Justice, said he hoped the succession would be peaceful.
He said: "We urge the Ethiopian People's Revolutionary Democratic Front to change for the good the political, democratic and human rights situation."
David Shinn, a former US ambassador to Ethiopia, said he expected many of Mr Meles's defence policies to remain.
Somalia's al Shabaab militants, who encountered Ethiopian troops twice under Mr Meles's tenure, hailed the former leader's death.
A spokesman said: "He led African leaders who had fingers in Somalia for two decades, but all in vain."
Mr Meles presided over a seven-year run of double-digit economic growth, advocating a mix of heavy state spending and private investment.
He was applauded for ploughing money into infrastructure but criticised by some for selling off swathes of land to foreigners. Many Ethiopians complain that his close business ties with China did not translate into more jobs.
International rights groups said Mr Meles was intolerant of dissent. He rounded up opposition leaders after disputed 2005 polls and several opponents and journalists have been arrested under an anti-terrorism law.
"Today is a day of joy for most Ethiopians and all freedom-loving people around the world," opposition website Ethiopian Review said, describing Mr Meles as a "genocidal tyrant".
State television said details of Mr Meles's state funeral would be announced soon.