Newby has joined the Magpies on a deal until the end of the 2018/19 season.
The 22-year-old has scored 19 goals in all competitions already this season.
Newby started out at Barrow AFC, coming through the ranks at the Furness Building Society Stadium to make several first-team appearances.
He also spent time on loan with Clitheroe`s league rivals Kendal Town in 2015/16.
Clitheroe boss Simon Haworth was left disappointed by the departure but can understand his reasoning, telling the club`s official Pitchero website: "Yeah I'm disappointed, but it's financially better for him and it's an opportunity to play in a higher league so we get that.
"Chorley have had him on trial before but chose not to take him, but obviously with the way he has played for us in recent games they are clearly very interested".
He has also made a handful of appearances for Barrow and Kendal Town.