The screenplay has been written by Eric Roth - who won an Oscar for Forrest Gump.
Leakey is former head of the Kenya Wildlife Service and was key to stemming the trade in illegal ivory.
"I've felt a deep connection to Africa and its culture for much of my life," said Jolie.
Leakey's extreme measures to tackle poachers, including sending helicopter gunships into the national park, have helped Kenya's elephant and rhino populations recover from the brink of disaster.
He made international headlines in 1989, when a stockpile of 12 tonnes of ivory was burned in Nairobi National Park.
Jolie said Africa is about "a man drawn into the violent conflict with elephant poachers, who emerged with a deeper understanding of man's footprint and a profound sense of responsibility for the world around him".
Producer David Ellison - whose company Skydance co-produced films including True Grit and Jack Reacher - called Leakey "inspirational," adding, "Africa is a story that deserves to be told".
Jolie's next movie, Unbroken, starring British actor Jack O'Connell is due in cinemas later this year.
She is currently directing and starring opposite her husband Brad Pitt in the film By The Sea, based on her own screenplay.

The decision to call off the match was taken at 12:35 GMT following an inspection at Sportsdirect.com Park where part of the League One club's pitch was still frozen.
The Latics are 22nd in the table and in the relegation places with Posh in sixth place.
There has been no announcement as to when the fixture will be rearranged.

The 22-year-old France-born winger, who has declared himself available for Algeria, joins for an undisclosed fee.
He spent five years with Le Havre, scoring six times in 60 games after moving from amateur club Quimper.
"I'm delighted we've been able to sign him. Any signing has to improve what we already have and Riyad is a very talented, technically good player," said Leicester manager Nigel Pearson.

They ruled that Attorney General John Larkin QC's bid came too late.
Mr Larkin sought to refer the verdict against Ashers bakery to the UK's highest court under devolution issues.
In October, the Appeal Court upheld a ruling against the bakery's Christian owners that their refusal to make a cake iced with the slogan "Support Gay Marriage" was discriminatory.
A long-running legal battle ensued when customer Gareth Lee sued after his order was declined at the company's Belfast city centre shop in May 2014.
The gay rights activist had requested a cake depicting Sesame Street characters Bert and Ernie with the slogan for an event to mark International Day Against Homophobia.
Bakery bosses refunded his money for the order because the message went against their Christian faith.
The McArthur family, who run the firm, insist their problem was with the cake and not the customer but Mr Lee claimed he was left feeling like a lesser person.
Last week, lawyers for the bakery were formally refused leave to appeal to the Supreme Court, though the McArthur family can now petition directly for a hearing in London.
Mr Larkin backed the family's case but his attempt to invoke his powers has now been rejected.
He was intending to ask the Supreme Court to rule on issues related to devolution.
Lord Chief Justice Sir Declan Morgan ruled in the Court of Appeal that this step came after the case had ended.
"We do not consider there are exceptional circumstances in this case which require us to re-open proceedings," he said.
Angelina Jolie has signed up to direct Africa, a film about celebrated conservationist Richard Leakey's battles with ivory poachers.
[NEXT_CONCEPT]
Oldham Athletic's League One fixture against Peterborough United has been postponed because of a frozen pitch.
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Leicester City have signed Riyad Mahrez from French second-tier side Le Havre.
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Northern Ireland's top law officer cannot refer the "gay cake" case to the Supreme Court, senior judges have said.