He will link up with the Magpies when his City deal expires at the end of the month.
The 19-year-old, who has been with the Premier League champions since the under-six age group has agreed a two-year deal at the League Two club.
Patching is yet to make a first-team appearance for City but was a regular at development squad level.
"I've never had an experience like this before," he told the club website. "I'm looking forward to it."
Patching added: "I can't wait to work under Kevin Nolan. He's got good attributes as a manager and he played in my position, so he can help me with a lot of things I need to work on.
"Hopefully I can go on to have a career like his."