Li is scheduled to also visit Nigeria, Angola and Kenya during the week-long trip, and give a keynote speech tomorrow at the Chinese-built headquarters of the African Union in the Ethiopian capital Addis Ababa.
The trip follows one Chinese President Xi Jinping made to the continent last year, shortly after taking office, a journey that underscored resource-rich Africa's importance to the world's second-largest economy.
"Ethiopia is the first stop because there is a deep friendship between our two countries and Ethiopia is a major country in Africa and the seed of African union," Li said in a news conference after his arrival and talks with Ethiopia Prime Minister Hailemariam Dessalegn.
Officials said the two premiers signed a number of legal accords covering diplomatic visa exemptions, cultural corporation and extradition, plus agreements on economic, trade and technical cooperation.
China's economic growth has been partially fuelled by African natural resources, including oil.
"China and Ethiopia have agreed on enhancing Ethiopia's industrialisation and on supporting Ethiopia's great vision to become Africa manufacturing house," Dessalegn said, hailing "many decades of strong economic and diplomatic relations".