She was best known for her role as Princess Leia in the Star Wars series.
Stars Wars' creator George Lucas said: "She was our great and powerful princess. She will be missed by all."
"Thank you Carrie Fisher for all that you've given us," tweeted the US Academy of Motion Picture Arts.
Her fellow Star Wars actor Mark Hamill called the news "downright heartbreaking," adding "Carrie was one-of-a-kind who belonged to us all - whether she liked it or not".
In New York, fans Eric and Elizabeth McCabe spoke of their shock at the news.
"She's a hero and will always be remembered as such," said Elizabeth McCabe.
"We grew up watching Star Wars and actually she looked pretty good in the last movie. We didn't realise that her health was so bad. It's really upsetting," added Eric.
Carrie Fisher's mother, the actress Debbie Reynolds, wrote on her Facebook page: "Thank you to everyone who has embraced the gifts and talents of my beloved and amazing daughter. I am grateful for your thoughts and prayers that are now guiding her to her next stop."
Star Wars co-star Harrison Ford described Fisher as "brilliant, original, funny and emotionally fearless".
Fisher's ex-husband, singer Paul Simon added: "Yesterday was a horrible day. Carrie was a special, wonderful girl. It's too soon."
Writer and actress Sharon Horgan, who cast Fisher as a cantankerous mother-in-law in the hit comedy series Catastrophe also expressed her sorrow at Fisher's death, calling her "fun, gifted, smart, kind, funny, funny, funny".
Speaking to BBC Breakfast, actor Warwick Davis - who played Wicket the Ewok opposite Fisher in Return of the Jedi - called her "a funny, warm person... who was very unaffected by fame".
Davis, who was just 12 when he played the role, added Fisher "had no airs and graces, I never saw her wanting to be treated like a celebrity."
Fans of the actress have been sharing stories with the BBC about meeting her, including John Moore, who remembers discussing mental health problems which she has admitted suffering.
"She has inspired me by teaching me that just because you're a little broken or a little different you can still be an inspiration and shine like she did.  She was honest about her health issues and was just herself.
"She taught me to not feel embarrassed or a lesser person just because you sometimes struggle to get through the day.  Her death has hit me hard but it also makes me feel so proud to have been like her, different."
The fans' princess
Fisher had been on tour promoting her latest book, The Princess Diarist, when she was taken ill as her flight back from London neared Los Angeles last Friday.
In a statement released on behalf of Fisher's daughter Billie Lourd, spokesman Simon Halls said: "It is with a very deep sadness that Billie Lourd confirms that her beloved mother Carrie Fisher passed away at 8.55 (16:55 GMT) this morning [Tuesday]."
The daughter of singer Eddie Fisher and Debbie Reynolds, Carrie Fisher made her film debut opposite Warren Beatty in 1975's Shampoo.
She also appeared in The Blues Brothers, When Harry Met Sally and Hannah and Her Sisters, and provided the voice of Peter Griffin's boss Angela in the adult animated sitcom Family Guy.
But her enduring fame is thanks to her role as Princess Leia in the original Star Wars trilogy, a part she reprised in last year's reboot The Force Awakens.
Discussing the part, she told the Daily Mail in 2011 that when she got the role in a "little science-fiction film", she just thought of it as a bit of fun.
"It exploded across the firmament of pop culture, taking all of us along with it. It tricked me into becoming a star all on my own."
She was also a successful writer, publishing several novels and memoirs, and working on the scripts for films like The Wedding Singer and Sister Act.
Her latest memoir, The Princess Diarist, contained revelations of an affair with Harrison Ford while the pair were shooting the first Star Wars film in 1976.
Fisher endured a difficult private life, and discussed her years of mental illness and drug addiction in interviews and writing. An early memoir was called Wishful Drinking.
The film industry and fans around the world have been paying tribute to the US actress and author Carrie Fisher, who has died aged 60 after a cardiac arrest.