Little is the last English manager to win a major trophy for an English club, when he led Villa to the League Cup in 1996.
The 53-year-old coach replaces Brian Carey, who has been removed from the helm of the side but stays on as first-team coach.
Wrexham are currently second from bottom in the Football League, after a late surge of four wins in five games saved them from relegation at the end of last season.
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Little said: "I'm delighted to be joining Wrexham.
"I think the most important thing is to sort out the team's position in the league. Then and only then can you look to the future.
"I know Brian Carey well and trust him because I signed him at Leicester.
"At the moment we need to get the club away from the bottom of the table, whether that takes a month or three months and once we do that we can look at other targets.
"The current position is not one where you can say that someone new can come in and we'll start flying up the league.
"It might take a little time and maybe it will be a long hard season, but we've got to have a focus on trying to get away from the bottom of the table.
"If that isn't the case straight away then we'll have to focus on retaining our league status. Those will have to be my initial aims.
"Some people are full of false promises early doors, but there has to be a realisation that the team are in a bad position.
"This is something I've inherited before at other clubs and it's something I think I've got experience in.
"The important thing is not to kid anybody and to stay focused but to pick up points steadily and move away from danger."
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