The 35-year-old supermodel is three months pregnant with her second child - believed to be due in August.
A source said: "It's true. Kate is pregnant. She's overjoyed at the news. She's passed the 12-week stage so she's telling more people."
Kate - who has six-year-old daughter Lila Grace with magazine publisher Jefferson Hack - has been dating The Kills guitarist Jamie Hince since March 2008.
The source said of Jamie, 39: "He's really excited at the prospect of becoming a dad. He already dotes on Lila Grace and is besotted with Kate.
"Kate and Jamie are closer now than ever. She's not going out as much as she used to but when she does he puts a protective arm round her."
The couple, who were reportedly in a panic after Lila's nanny pulled out of a forthcoming family trip to South Africa, have decided to use the holiday to spend quality time with Kate's daughter.
A source said: "They have decided it will be low-key, not much partying, and they'll have a lot of family time with the three of them."
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