The 43-year-old defender has agreed to take over at the Premier Division club.
He will be joined by coaches Shaun Gardner, Lee Dodgson and Neil Uberschar, goalkeeping coach Stu Parkin and physio Liam Enright.
A club spokesman said: "The club's committee is delighted to announce Garry Thompson has been appointed as first team manager with immediate effect.
"Garry comes with a wealth of experience within the game having played over 700 games from Conference through to the Championship.
"Garry is also bringing an experienced back room staff to help him move the club forward."
Kendal-born Thompson has previously played at Morecambe, Scunthorpe, Notts County, Bradford City and Wycombe Wanderers.
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