He will be available to make his debut in Saturday's league visit to Trafford FC.
Reece is aged 19 and was originally with Birmingham City. He made his first team debut in an F A Cup tie at Leeds United in January 2013.
He had a loan stint with Worcester City in the Conference North in October 2013 before being released by the Blues at the end of last season. He subsequently signed for Kidderminster Harriers following successful trials in July 2014.
Welcome to the club Reece!
Last week Alex Dallison left the club and the teenage defender has now signed for Chasetown. We wish him well with his new club.