Flanagan was offered improved terms but has elected to move to the Trico Stadium.
The 27-year-old had been with Hednesford since October 2020.
He had joined another of the Pitmen`s rivals, Rushall Olympic, from Vanarama National League North side Leamington in October 2019 and then switched to another, Stratford Town, in January 2020.
He was tempted back to the Brakes on a permanent basis in September 2018 having spent a loan spell with Leamington as a 19-year-old in their first season in the Conference North (2013/14), making a big impression in the final eight games of the season, scoring twice.
A product of the Walsall academy, he went on to break into the Saddlers' first team the following season and made nearly 50 appearances in League One prior to his release in the summer of 2018.
He was very unfortunate to miss the entire 2016/17 campaign after rupturing his anterior cruciate ligament, and then dislocating his shoulder during his comeback game 10 months later.
Redditch manager Matt Clarke told his club’s website: "Reece is a huge signing for the club. He was outstanding for Hednesford last season. Reece is exciting to watch and will no doubt be a future fan’s favourite. He brings excellent pedigree and the type of player we want to attract to the football club as we strive to improve and progress as a team. We managed to get his signature over the line ahead of many of our local rivals which, in itself, shows the progress we have made over the last couple of years”.
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