The Clarets have splashed out over £20m to land Ugochukwu, who has penned a contract to 2030.
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"It's a great feeling to sign for Burnley," said Ugochukwu.
"As soon as I was made aware of the club's interest in signing me, I was keen to hear more about the project. I spoke to the manager and Maxime (Esteve) – they were both so passionate about the club and the direction it's heading in.
"It feels like this is the perfect move for me at this stage of my career with the ambition the club is showing."
Ugochukwu spent two years at Chelsea, making 15 appearances. Last season, he was on-loan with Southampton.