The show's two-hour pilot was recently filmed on location in Botswana by Oscar-winning director Anthony Minghella, who helmed "Cold Mountain" and "The English Patient," The Weinstein Co. said.
Minghella wrote the script with Richard Curtis. The pair is also executive producing the series.
In addition to the two-hour pilot, HBO has ordered 13 one-hour episodes that will begin filming this summer, with HBO obtaining U.S. and Canadian television and home video rights, and the BBC taking U.K. television distribution. The Weinstein Co. controls all other international territories.
"Alexander McCall Smith's wonderful books have been a sensation around the world for years, and we're thrilled to be teaming up with the BBC and The Weinstein Company to adapt these highly entertaining stories," Richard Plepler, co-president of HBO, said in a statement Monday.