This latest win follows her triumph in the Brits Rising Star Award in December.
Celeste received 30 first-place votes from the 170 pundits who voted for the Sound of 2020.
Indie band Easy Life came second and pop-punk agitator Yungblud was named third in the poll.
Celeste was born in Los Angeles and raised in Brighton, where she started making music as a teenager.
The British-Jamaican singer wrote her first song at 17 and has subsequently supported acts including Janelle Monáe, Neneh Cherry and Michael Kiwanuka.
Celeste says: ‘I'm really, really happy. It's like all of the work that went in throughout the [last] year wasn't invisible. I can't wait now to see what the rest of the year will look like. I'm so thrilled and so excited. I can't wait.’
BBC Radio 1 DJ Annie Mac comments: ‘Her songwriting is personal and poignant but with universal appeal. I think she could easily join the long list of Sound Of winners who went on to be global stars.’