Cotterill, who has also had spells as manager of League of Ireland side Sligo, Cheltenham and Stoke, has been out of work since leaving Turf Moor in 2007.
He admitted his appointment had come out of the blue but insists his long absence from the game will not be a problem and that the opportunity to return to management at Meadow Lane was too good to turn down.
"I need a couple of days to get my feet under the table but the aim is to keep winning, because if we keep doing that then promotion will come and that is still the ultimate aim," Cotterill told the club's official website.
"There are some good players here that have been playing good football and I don't want to change that.
"I might not need to make any changes but if I do make changes hopefully they will be improvements. But this is a great club and I just can't wait to get going.
"I am still looking at things because it has all happened so quick. I got a phone call off (chief executive) Jim Rodwell at 6pm on Sunday night.
"He asked me what I'd been doing and I explained that, although I've been out of the game for a while, I know exactly what has been going on.
"He said 'Did I fancy meeting in London on Monday morning?', I did and I was offered the job on the way home in the car. I accepted straight away.
"I think the opportunity to win made it impossible to turn down as there aren't many jobs like that.
"There is a good set of players and a good team spirit and if we can build on that and add to it we will hopefully achieve the ultimate aim of promotion."
Notts County also announced on Tuesday that the club will avoid going into administration this season.
The club were due back in the High Court on Wednesday to face a winding-up petition from HM Revenue and Customs over an unpaid tax bill.
However, new owner Ray Trew revealed in a statement: "It has always been our intention to avoid administration, which may have been an easier option but would have caused considerable harm to the local companies that have shown great faith and support in this club in recent years.
"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 on this matter.
"We now hope to move on from the troubles of the past, to focus on making Notts County Football Club a viable and attractive sporting institution once again and to build on our illustrious history to shape a brighter future for this great club."
The club also revealed that they had agreed terms with Nottingham Rugby for them to groundshare Meadow Lane for the next seven years.
Source: Team Talk
Source: Team Talk