The first film of the series will be titled Fantastic Beasts and Where to Find Them.
Warner Bros said the film series was part of an “expanded creative partnership” with the best-selling author.
The eight Harry Potter films are the largest-grossing film franchise in history.
The new film will feature Newt Scamander, the fictional author of the textbook Fantastic Beasts and Where to Find Them, owned by Harry Potter at Hogwarts school.
Warner Bros has given no indication as to when the film could go into production.
“It all started when Warner Bros came to me with the suggestion of turning Fantastic Beasts and Where to Find Them into a film,” said Rowling.
“I thought it was a fun idea, but the idea of seeing Newt Scamander, the supposed author of Fantastic Beasts, realised by another writer was difficult.
“Having lived for so long in my fictional universe, I feel very protective of it and I already knew a lot about Newt. As hard-core Harry Potter fans will know, I liked him so much that I even married his grandson, Rolf, to one of my favourite characters from the Harry Potter series, Luna Lovegood.
She went on: “As I considered Warners’ proposal, an idea took shape that I couldn’t dislodge. That is how I ended up pitching my own idea for a film to Warner Bros.
“Although it will be set in the worldwide community of witches and wizards where I was so happy for 17 years, Fantastic Beasts and Where to Find Them is neither a prequel nor a sequel to the Harry Potter series, but an extension of the wizarding world.
“The laws and customs of the hidden magical society will be familiar to anyone who has read the Harry Potter books or seen the films, but Newt’s story will start in New York, 70 years before Harry’s gets underway.”
Rowling added: “I always said that I would only revisit the wizarding world if I had an idea that I was really excited about and this is it.”
Warner Bros also announced that it would serve as the worldwide TV distributor (excluding the UK) for the upcoming BBC TV adaptation of Rowling’s recent adult novel The Casual Vacancy. It is expected to air in 2014.
More than 450 million copies of Rowling’s seven Potter books have been sold worldwide.
She also wrote two small volumes, Fantastic Beasts and Where to Find Them and Quidditch Through the Ages – both named after Harry’s schoolbooks within the novels. They were published in March 2001 in aid of Comic Relief.
Another Potter spin-off book, The Tales of Beedle the Bard, followed in December 2008.
The Harry Potter novels, about a boy wizard who survives the attack that kills his parents, became a worldwide phenomenon and were turned into eight blockbuster Warner Bros films starring Daniel Radcliffe.
The films have grossed more than $7.7bn (£4.8bn) to date worldwide at the box office, making Harry Potter the largest-grossing film franchise in history.