According to Us Weekly magazine, the 65-year-old star told his daughters Kendall and Kylie Jenner and step-daughters Kourtney and Khloe Kardashian and Kim Kardashian West that he was transitioning into a woman on 19 January, the same day Khloe posted a family picture on Instagram, in an upcoming episode of the reality show.
A source told the publication: "He literally started the conversation with, 'Hey, guys, I'm becoming a woman, but I'm sure you probably already figured that out.'"
The former Olympian reportedly got "a little emotional" during the conversation, which is set to air in episode 13 of the new Keeping Up with the Kardashians series , and is said to have told his family to simply say, "Bruce is in a very good and happy place", if they were asked about him.
The source added: "There was so much speculation, and they were all wondering about the truth. Bruce had to address it with them.
"He got a little emotional, but it wasn't a jaw-dropping conversation, it's a surprise to the girls that he's doing this at 65."
Bruce is also said to have asked his children to stop calling him Bruce and asked them to refer to him as the new name he has chosen.
Kylie, 17, and Kendall are said to be very supportive and the 19-year-old model told her father to "just be you".
A source said: "They want nothing more than for their dad to enjoy the life he wants to live."
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