The 32-year old Brazilian-born ex-Japan international spent five years with the Reds (along with a short stint with Red Bull Salzburg) but has moved on to the club's J-League rivals.
Nagoya are still alive in the Asian Champions League quarter-finals and are looking to add to their squad.
"I'm so glad that I have been able to sign with Nagoya," Santos said in a statement.
"I'll work hard to meet the expectations from the manager, team-mates and supporters here."
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