Acting Prime Minister Hailemariam Desalegn said the building would include a library and an exhibition of Meles Zenawi’s life and achievements.
Thousands of people, including dozens of foreign leaders and dignitaries, attended Sunday’s funeral.
The ex-prime minister died last month in Brussels after 21 years in power.
The cause of the 57-year-old’s death has not been announced.
Meles Zenawi was praised for bringing development to Ethiopia, which has long been associated with hunger and famine.
However, he was criticized for cracking down on opposition parties, the media and civil society groups.
The government has also set up a website in his honor.
Meles Zenawi’s flag-draped coffin was carried from his palace in the capital Addis Ababa to the city’s Meskel Square for a ceremony, then buried at the Holy Trinity Cathedral.
Leaders including South Africa’s Jacob Zuma, Benin Boni Yayi representing the African Union and US ambassador to the UN Susan Rice praised Meles Zenawi.
“He wasn’t just brilliant, he wasn’t just a relentless negotiator and a formidable debater, he wasn’t just a thirsty consumer of knowledge – he was uncommonly wise, able to see the big picture and the long game, even when others would allow immediate pressures to overwhelm sound judgement,” said Susan Rice.
Microsoft founder Bill Gates also attended the funeral, as did Sudan’s President Omar al-Bashir – who has been indicted by the International Criminal Court on several counts of war crimes.
Meles Zenawi was a close Western ally and twice sent troops into neighboring Somalia to tackle Islamist militants.
Hailemariam Desalegn is to remain prime minister until the next elections, due in 2015.
Meles Zenawi:
• Emerged from Tigray People’s Liberation Front (TPLF), which carried out armed struggle against communist military regime in 1970s and 1980s
• Became president in a transitional government in 1991 and then prime minister in 1995
• Married another TPLF veteran, Azeb Mesfin, and had three children
• Under his leadership, a closed and secretive country gradually opened to the outside world
• But reputation tarnished in 2000s amid increasing repression in Ethiopia
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