Muto was not an automatic recipient, which meant he had to wait until an FA Governing Body Endorsement hearing.
It was a positive outcome for the club, who were able to complete the £9.5 million transfer from Mainz.
"I am really looking forward to playing in front of the fans," Muto is quoted as saying by Sky Sports.
"I hope to achieve good results - that is what I am here to do. I would like to perform well and leave my name in Newcastle's history."
He becomes the club's fifth signing in this transfer window.