The 54-year-old actress heard the big news while appearing onstage at Raleigh Supercon in North Carolina and was visibly shocked.
Broadchurch star Whittaker will become the first female actress to take on the role, but Kingston, who played the Doctor's wife River Song, announced that it is a "marvellous" casting.
After a fan in the convention audience shouted out the news, Kingston gushed: "Jodie Whittaker? Oh my goodness!" before making kissing noises.
She continued: "I’m always the damn cradle-snatcher! Oh, that’s lovely. She’s a really great actress. She’s fantastic.Related articles
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Oh, that’s lovely. She’s a really great actress. She’s fantastic