Cox moves to Shrewsbury on-loan to the end of the season.
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"Matt is someone we've been aware of for a while," Salop head coach Michael Appleton said.
"He's got a great pedigree and a strong background in terms of footballing education.
"He's good with his feet, has impressive distribution and we're excited to bring him in.
"He is going to be able to challenge Will (Brook) for a place in the starting 11, which is healthy for both players and the squad."