Charlie Redmayne, head of her publisher HarperCollins, said she was "a wonderful and inspiring person who was much loved by everyone".
Kerr, who published more than 30 books over a 50-year career, dreamed up the tiger to amuse her two children.
Charlie and Lola author Lauren Child said she was a "huge admirer of her work, as a writer and an illustrator".
Redmayne added: "She was a brilliantly talented artist and storyteller who has left us an extraordinary body of work.
"Always understated and very, very funny, she loved life and loved people - and particularly she loved a party."
He said that "time spent in her company was one of life's great privileges and I am so grateful to have known her".
As a child of the pre-war German intelligentsia, Kerr was forced to flee with her Jewish parents when Adolf Hitler came to power.
The family came to London, via Paris, in 1936 when Judith was 13.
Francesca Simon, author of the Horrid Henry children's books, told BBC Radio 5 Live she was "feeling so sad about this".
"The fact that she was in her 90s and still so engaged with children's books, and the fact that she came to this country as a refugee and the life that she led."
She said of Kerr's famous Tiger tale: "It is a perfect book, because it is a mysterious book.
"On the surface it's a very simple story. It's a tiger who comes in, and is this guest who you're not sure about. But her stories also have this undertone of emotion, which is I think why we keep going back to them, to kind of delve into their mysteries.
"As well as the most beautiful and glorious illustrations. Her artwork is fantastic.
'Forever in our imaginations'
"And I love, as a writer myself, that she was writing and illustrating up to the end. In fact I was just trying to get tickets to see her at Hay-on-Wye next week. So I love her continuous engagement with her profession. To me that's unbelievably inspiring."
BBC Newsnight presenter Emily Maitlis once asked Kerr if there was any layered meaning beneath The Tiger Who Came to Tea, but was set straight by the author.
TV talk show host Jonathan Ross described her most famous work as being "a huge part of my children's life and I loved reading it for them."
"I doubt there is a more perfect children's book then The Tiger who came to Tea," he tweeted.
Spandau Ballet's Gary Kemp tweeted his gratitude for Kerr's creations.
"Goodbye Judith Kerr," he said, "All my four boys have adored you and I've loved reading your work to them. Forever on our bookshelves and in our imaginations."
Fellow writer Tony Parsons also added his voice.Kerr's publisher at HarperCollins, Ann-Janine Murtagh, said it had been "the greatest honour and privilege to know and publish Judith Kerr for over a decade", describing her as a person who "embraced life as one great big adventure and lived every day to the full".