The defender moves to the Premier League new-boys as he comes off contract at Portman Road.
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Tuanzebe has signed a one-year contract with the Clarets.
"It became a very simple decision after speaking to the manager and the message was very clear, precise and straight to the point," said Tuanzebe.
"It's a new chapter for me, back in the vicinity of Manchester and home and I'm ready to continue my journey now at Burnley."