Nottingham-based Bertram, 30, has had two spells at the Raygar Stadium sandwiched around a season at Ilkeston Town.
He began his non-league career at Basford United and has also played for Carlton Town in the Northern Premier League.
Standing at six-foot plus, he is a tough-tackling midfielder who can also operate in defence so he offers valuable versatility to manager Paul Phillips.
“Riece can play the holding midfielder and there may be times we need him to slot in alongside Leesy (Mark Lees),” Phillips explained ahead of Tuesday’s game with Grantham Town.
Suspensions for two Chesterfield players confirmed ahead of key clashes against Aldershot Town, Wrexham and Notts County
Latest National League transfers as Scunthorpe United, Southend United and York City all do business
Former Sheffield United and Wealdstone striker signs for Matlock Town ahead of new season
'Frailties' - Aldershot Town boss highlights weaknesses ahead of Chesterfield visit
'Intriguing': Chesterfield's squad numbers announced - seven talking points
“But he can also play as a centre-half which gives us a little more leeway, and now we’re going to lose Ryan Qualter for three games after his sending off on Saturday, in hindsight it gives us more cover there.
"He offers us versatility and flexibility in the defensive area. Also we’ve asked a lot of Leesy and if anything happens to him, we’ve got Riece.”
Phillips added that he has had his eye on Bertram for some time.
He said: “We put seven days in on him a while back, he spoke to his manager and has decided to make the move here.
"He knows that like anyone else, he’ll have to fight for his place but I’m delighted to have him on board.
Bertram was expected to feature in Matlock’s home clash with Grantham Town on Tuesday night.