The former Bournemouth and Gillingham player was most recently managing the Gills until last month.
Pennock returns to Non-League having first spent two years as manager of Welling United in 2005 before leaving in 2007 to take up a coaching job at Stoke City under Tony Pulis.
He left in 2013 and was appointed manager of Forest Green Rovers where he remained for three years.
A statement from Barrow read: “We are delighted to have Adrian onboard. It quickly became clear that he was the stand out candidate, having met with him at our games against Ebbsfleet and Chester.
"We are convinced that he can lead us forward, to climb up the table and help us build the club in the community as well.”