Prime Minister Narendra Modi made the announcement during a speech in the Ugandan parliament — the first by a serving Indian prime minister.
The latest sign that the Asian state is seeking to strengthen its presence on the continent.
6,000 Indians serve in UN peacekeeping missions in Africa.
India will open 18 new embassies across Africa, Prime Minister Narendra Modi told Uganda's parliament on Wednesday during a charm-offensive tour of the continent.
Rounding off a two-day visit to Kampala, Modi also announced the donation of a badly-needed cancer therapy machine and loans worth $200 million (171 million euros) for infrastructure and environmental projects.
India, the world's most populous democracy, is vying for influence in Africa with its regional competitor China which has aggressively developed trade, financial and diplomatic ties on the continent.
India currently has 29 full diplomatic missions in Africa, according to Delhi, compared to China which has 50.
It hopes to open its new missions within three years, according to an Indian official who did not confirm which countries would receive envoys.
Modi also praised Ugandan President Yoweri Museveni for welcoming back the so-called Uganda Asians who were expelled by despot Idi Amin Dada, who was in turn ousted by Museveni.
"Your visionary leadership has enabled Ugandan people of Indian origin to return to their cherished home, regain their lives and help rebuild the nation that they deeply love," Modi told a crowded parliament chamber, becoming the first Indian prime minister to address the legislature.
Keen to be seen as a friend to Africa, Delhi plays up a shared history that China lacks, citing 16th-century merchants who plied Africa's coastline and India's fight against colonialism.
Earlier this week, Modi visited Rwanda where he symbolically donated 200 cows to poor families and oversaw Indian loans to Kigali.
He flew to South Africa from Uganda for a summit of the BRICS bloc.
The gathering in South Africa will bring together the leaders of Brazil, Russia, India, China and South Africa (BRICS) for talks overshadowed by the looming US-led global trade war.