President Barack Obama.Getty

The US leader has lent his support to the former Olympian - who was known as Bruce Jenner before undergoing gender transition treatment - and her "story".

Responding to a tweet from Caitlyn introducing herself, the president wrote: "It takes courage to share your story. Your story matters in the fight for LGBT rights."

A huge number of stars have spoken out on Twitter to support Caitlyn since her new female identity was unveiled in Vanity Fair magazine.

Singer Lady Gaga wrote: "Caitlyn, thanku for being a part of all our lives & using your platform to change people's minds... The beauty on the inside is now also on the outside. God bless you and the whole family for sharing it with us (sic)"

Meanwhile, actress Demi Moore praised the 'Keeping Up with the Kardashians' star for her "beautiful authentic self", while Susan Sarandon congratulated Caitlyn on her "rebirth".

Demi wrote: "Thank you @Caitlyn_Jenner for sharing the gift of your beautiful authentic self inside and out!"

Susan posted: "Congratulations @Caitlyn_Jenner on your rebirth. You've inspired so much intelligent dialogue and courage."

Talk show host Ellen DeGeneres praised the 65-year-old star for her "bravery" and 'Girls' star Lena Dunham made a joke.

Ellen wrote: "My hope for the world is that we can all be as brave as @Caitlyn_Jenner."

Lena quipped: "I just want Caitlyn Jenner to take me out and teach me how to drive a stick shift in heels."

Other stars who posted messages of support included Kerry Washington, Jenny McCarthy and Alyssa Milano.