The actress – most famous for her role as Beth Latimer in Broadchurch – was revealed in a clip played after the Wimbledon men’s final, as she becomes the first woman to take on the role.
Jodie said in a statement: “I’m beyond excited to begin this epic journey – with Chris and with every Whovian on this planet.
“It’s more than an honour to play the Doctor. It means remembering everyone I used to be, while stepping forward to embrace everything the Doctor stands for: hope. I can’t wait.”
New showrunner Chris Chibnall added: “After months of lists, conversations, auditions, recalls, and a lot of secret-keeping, we’re excited to welcome Jodie Whittaker as the Thirteenth Doctor.
“I always knew I wanted the Thirteenth Doctor to be a woman and we’re thrilled to have secured our number one choice. Her audition for The Doctor simply blew us all away.
“Jodie is an in-demand, funny, inspiring, super-smart force of nature and will bring loads of wit, strength and warmth to the role. The Thirteenth Doctor is on her way.”
Outgoing Doctor Peter Capaldi added: “Anyone who has seen Jodie Whittaker’s work will know that she is a wonderful actress of great individuality and charm.
“She has above all the huge heart to play this most special part. She’s going to be a fantastic Doctor.”
Charlotte Moore, Director of BBC Content said: “Making history is what Doctor Who is all about and Chris Chibnall’s bold new take on the next Time Lord is exactly that. The nation is going to fall in love with Jodie Whittaker – and have lots of fun too!”
Piers Wenger, Controller BBC Drama also said: “Jodie is not just a talented actor but she has a bold and brilliant vision for her Doctor.
“She aced it in her audition both technically and with the powerful female life force she brings to the role. She is destined to be an utterly iconic Doctor.”
It comes as Peter Capaldi and former Doctor Who stars Billie Piper and Karen Gillan called for the new Time Lord to be a woman.
Writer Mark Gatiss has also said it is the perfect time for an actress to take on the lead role in the show.
Fleabag creator Phoebe Waller-Bridge and Broadchurch star Jodie Whittaker are among the actresses who have been backed for the role.
Capaldi’s decision to step down sparked speculation that the next incumbent could be female after he said he would like to see a woman take his place.
Shortly after announcing his decision he told BBC Radio 2: “The time felt right to bow out, to let somebody else play this wonderful role and I would like Frances de la Tour to be the first female doctor.”
De la Tour, 72, has a 50-year acting career behind her and is best known for playing half-giantess headmistress Madame Olympe Maxime in the Harry Potter films and landlord Rigsby’s tenant Ruth in 1970s comedy series Rising Damp.
Actress Billie Piper, who played companion Rose Tyler, ruled herself out of becoming the first female doctor, saying the responsibility would be “too enormous”, but added her vote would be for Captain America star Hayley Atwell.
Describing her as a "sassy" option, Piper previously told the Press Association: "She would be amazing."
Meanwhile, Gatiss has said: "I would love it to be a woman, I think it would be marvellous.
"Not through pressure of political correctness but it sort of just feels like it's time. I think it would just be great. The show is not the new kid on the block anymore.
"It's been back for 12 years and I think it would just be really thrilling, but a lot of people disagree but I just think, why not?"
Gillan, who played companion Amy Pond for two years alongside Matt Smith's Doctor, has also added her voice to the call, saying: "It would be cool to see a woman in the role one day because a woman could absolutely play that role."
The new actor will make their debut in the Christmas special which is set to air on Christmas Day.