Cotterill will replace current current caretaker boss Dave Kevan, who was assistant manager under Cotterill at Turf Moor between 2004-2007, on a deal running until the end of the season.
In a club statement, Trew said: "It has always been our intention to avoid administration, which may have been an easier option.
"My staff and I have been working tirelessly to not only assess the club's finances but also to work out how best to resolve the underlying issues that exist and I am delighted to have reached the stage where I can make an informed decision.
"We now hope to move on from the troubles of the past, to focus on making Notts County a viable and attractive sporting institution once again."
Former caretaker boss Dave Kevan will now renew his partnership with Cotterill in the assistant manager role at Meadow Lane.
Trew added: "Steve Cotterill is a man that we know plenty about and who was always top of our list of preferred managers when we first took over Notts County.
"Steve brings with him a wealth of experience both as a player and manager and I believe that he has the pedigree to take this club forward."
Source: Team Talk
Source: Team Talk