Radcliffe, who played the boy wizard in the film series, is taking part in the starry lockdown reading initiative Harry Potter At Home.
Eddie Redmayne and Stephen Fry are among the other celebrities involved.
The videos will feature on Rowling's online hub to help children, parents, carers and teachers through the crisis.
Audio versions will also be available on Spotify.
Each celebrity will read a different section of Harry Potter and the Philosopher's Stone - known as Harry Potter and the Sorcerer's Stone in the US.
Radcliffe kicked off the series on Tuesday, telling how a baby Harry is left on the doorstep of his aunt and uncle.
Radcliffe reads the famous opening lines from his couch: "Mr and Mrs Dursley, of number four, Privet Drive, were proud to say that they were perfectly normal, thank you very much."
It provoked immediate excitement from fans on Twitter.
"This made my quarantine," said one, Fran Radson Driver.
Readings of all 17 chapters of the book will be released weekly between now and the middle of the summer.
Harry Potter at Home was launched by Rowling and Wizarding World Digital as a response to the Covid-19 pandemic, and offers quizzes, puzzles and a fan club.
Speaking last month, the author said she launched it because "parents, teachers and carers working to keep children amused and interested while we're on lockdown might need a bit of magic".