Author Rosie Rowell and her editor Emily Thomas were named the winners at a ceremony at Walker Books in London.
The judges said the book was "a work of originality, power and intelligence" that had deserved greater attention.
The Branford Boase is the only award to recognise the role of the editor in nurturing new talent.
Leopold Blue, published by Hot Key Books, is set in a small backwater town in South Africa in 1993 where the story of 15-year-old Meg plays out against a backdrop of political change.
"In Leopold Blue the judges have found a work of originality, power and intelligence that seems surprisingly to have escaped the notice it deserves," said Julia Eccleshare, chair of judges, and children's books editor of The Guardian.
"The characters and setting are brilliantly observed and described, and all readers will recognise something of themselves in Meg. The background gives it particular depth and it transcends the coming-of-age genre."
Rowell, who was born and grew up in Cape Town, said it was "an enormous honour" to win.
"It is a confirmation that our stories matter. Everyday people, struggling in their own ways, whether they are stuck in dead-end tiny towns or trying to find their way in big cities are no less important than the heroes that dominate the news. We all have a story that is worth telling."
The author, who now lives in West Sussex, had her second novel, Almost Grace, published in June.
The Branford Boase Award - worth Â£1,000 - was set up in memory of the prize-winning author Henrietta Branford and her editor Wendy Boase - who both died of cancer in 1999.
Previous winners include Marcus Sedgwick, Philip Reeve, Annabel Pitcher, Frank Cottrell Boyce, Siobhan Dowd and Patrick Ness.
The other titles on the 2015 shortlist were:
Leopold Blue, a coming-of-age story set in South Africa, has won the 2015 Branford Boase Award for an outstanding debut children's novel.