"Ours is a relationship forged in the crucible of the shared struggle against imperialism, colonialism, racial discrimination and apartheid. That era is now behind us, but the solidarity engendered by that shared struggle continues," she said.
The minister also described the summit meeting between India and the 54 countries of Africa as a "family reunion".
"This gathering of African heads of state and heads of government is like a family reunion. And I can see how the diversity of Africa matches our own, how every flag from Africa has its own special place," she said.
Sushma Swaraj said the modern partnership between India and Africa rested "on the pillars of economic growth, development and empowerment and is a consolidation of our engagement at various levels - bilateral, regional and pan-African".
"The longstanding and multifaceted India-Africa development partnership is based on the principles of equality, friendship and solidarity. It represents one of the finest examples of South-South cooperation," she said.
She ended her speech with an African proverb: "If you want to go quickly, go alone. If you want to go far, go together."
The IAFS is an initiative between India and Africa Union nations to increase trade and investments, with India looking to near China's bilateral trade of over $200 billion with the continent.
"This (summit) is going to take relations between India and Africa to new heights," Prime Minister Narendra Modi later told reporters.
The event is said to be one of the largest gatherings of African leaders abroad, with over 1,000 delegates representing the 54 African union nations.