The book was the first in Ferrante's hugely successful Neapolitan quartet, which tells the story of a complicated friendship between two brilliant women that begins in a poor neighbourhood in post-war Naples.
HBO said in a statement that the author, who uses Elena Ferrante as a pseudonym, participated in the adaptation of the saga for the eight-episode production, which will be filmed in Italian.
Casey Bloys, HBO's president of programming, said they were excited "to bring the powerful, epic storytelling of Elena Ferrante and her Neapolitan Novels to life."
Although they have won no major literary prizes to date, the novels were a publishing sensation and translated into dozens of languages, sparking intense public interest in the author's true identity.
Italian journalist Claudio Gatti recently claimed that evidence he had uncovered pointed to Anita Raja, a Rome-based translator, as the writer.
But a row subsequently erupted over journalistic ethics and writers' right to protect their identities.
Italian director Saverio Costanzo, known for "The Solitude of Prime Numbers" (2011), will direct the series, while Italian companies Wildside and Fandango are also participating in the production.
"Producing a series based on the incredible work of Elena Ferrante is an exciting challenge," said Wildside CEO Lorenzo Mieli.
"Through the eyes and lives of two extraordinary friends, her quadrilogy describes 50 years of Italian history, touching on universal themes and feelings."
Antonio Campo Dall'Orto, RAI's director general, said the project "satisfies many of the public service's objectives in the field of TV drama.
"It is Italian and international; it is universal but complex; it is a huge co-production with a global value," he said.