Fofana moved to Stamford Bridge on a six-year deal in January 2023 from Norwegian side Molde.
He spent the first half of the season on loan at Union Berlin in Germany, making 17 appearances, and scoring in the Champions League group stages against Napoli.
The 21-year-old said Burnley will be the “perfect” club for him to progress.
He added: “To work with [Clarets boss] Vincent Kompany will be very good. I have seen a couple of games already and I think this is the right place for me to make the next steps.”
Fofana’s loan deal is subject to approval from the Premier League and Football Association.
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