Greenfield, 19, joins the club from National League North side Gateshead on a short-term loan, and has already impressed in games against Sheffield and Tamworth.
He said: "I’m delighted to be at Matlock Town. As soon as the opportunity came about to come on loan, it was a no brainer.
"The gaffer and the lads have welcomed me in straight away. The two games I’ve played have both been really good tests and have shown just how good we are as a team,.
"I can’t wait for the season to start Saturday in the FA Cup which will be good start to hopefully a successful season.
"I’m looking to make a big impact in the team with consistent performances and getting the goals and assists to help the team as much as possible."