The club announced last month that Benitez would leave when his contract expired on June 30.
The 59-year-old was expected to depart after failing to agree a contract extension with owner Mike Ashley over the last few months.
The former Liverpool and Real Madrid boss joined Newcastle in March 2016, but failed to save them from Premier League relegation. He stayed with the club in the Championship and led them back to the top flight the following season.
They finished 10th in their first year back up and 13th last season.
Benitez thanked the fans for "three fantastic, exciting and, at times, challenging years".
"I wanted to stay, but I didn't just want to sign an extended contract, I wanted to be part of a project," he said on Twitter.
"Unfortunately it became increasingly clear to me that those at the top of the club did not share the same vision."
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