The 23-year-old has agreed a contract until June 2007 with the fee rising to £15,000 when the England non-league international plays his 20th game.
Cowan played 11 games for Canvey this season before falling out of favour and joining Nuneaton Borough on loan.
"Barnet had come in for me a couple of times, and Aldershot, but the chance of league football is too much to turn down," he told the Shrews' website.
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MMIX
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