‘The World Reimagined’ will be on display at 10 locations across the city, between August 13 and October 31.
The project, which will take the form of a trail, aims to educate about issues such as the slave trade and the contribution of black culture and music to modern Britain.
The globes themselves have been designed by 10 different artists from across the UK and the exhibition is going on display in six other cities around the country this summer.
Documents attached to the planning application for the sculptures, submitted by The World Reimagined, said: “We are living in a key moment for racial justice and it calls on us to courageously face our shared history with honesty, empathy and grace so we can create a new future in which all can say: I am seen.
“That is the mission of The World Reimagined.
“The trails will be the centre of a broader education and engagement programme, with hundreds of schools, community groups, sporting and cultural institutions across the country.
“The World Reimagined is a vibrant project that will inspire and instill pride in what it means to be black and British and help us all better understand what itmeans to be British.”
One of the founders behind the project is Yinka Shonibare, who is also creating a sculpture dedicated to the memory of David Oluwale, that will be put up in Leeds next year.
Mr Oluwale drowned in the River Aire in 1969 after being subject to repeated racial harassment from police officers.
Councillor Jonathan Pryor, Leeds City Council’s deputy leader and executive member for culture, said: “This is a fantastic opportunity for our city to be part of a national art project which provides a platform for our diverse communities to come together to share their stories, have conversations and reimagine a future Leeds and a future world where everyone’s diversity and cultural heritage is recognised and celebrated.
“We look forward to welcoming ‘The World Reimagined’ trail to our city.”