Johnson was until recently part of the management team at AFC Wulfrunians.
Chairman Mick Murphy said: "I am well pleased that Matt has joined the club as First Team Manager he brings a wealth of playing and coaching experience to MDTFC.
"Matt is well aware of the task that lies ahead in securing safety from relegation. The appointment of a new Manager has taken some time, but I needed to ensure that we made a first class appointment."
First team coach Steve Chamberlain will continue to be a major part of the club's coaching team.
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