The celebrity chef - who appeared on the US Food Network  - died in her home in New York on Tuesday, her family said.
"Her smile lit up every room she entered," her family said in a statement to E! News.
"Anne's light radiated far beyond those she knew, touching millions across the world.
"Though she is no longer with us, her warmth, spirit, and boundless love remain eternal."
New York police said she was found unconscious in her Brooklyn apartment and pronounced dead once emergency services arrived.
A cause of death is yet to be confirmed.
The Food Network said on Instagram: "Anne was a remarkable person and culinary talent, teaching, competing and always sharing the importance of food in her life and the joy that a delicious meal can bring."
Supermodel Gigi Hadid - who teamed up with Burrell on cooking competition Beat Bobby Flay in 2023 - admitted she is "heartbroken" by the news.
Former Top Chef star Carla Hall hailed the late chef as an "incredible" mentor.
"Anne was an incredible cook and teacher. FIERCE! She will be missed," she wrote.
Burrell's TV career started 20 years ago alongside Mark Ladner on a pilot for Food Network's Iron Chef America series.
She was soon hosting her own shows, including Secrets of a Restaurant Chef and Works Cooks In America, with the latter running for the past 15 years.
with AP
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