The former Germany international was on the coaching staff at MK Dons and Leicester last season and has now chosen to begin his managerial career with non-league County.
The Cheshire club saw their 105-year run in the Football League end last season as they were relegated from League Two.
But the Hatters will be hopeful of bouncing back at the first attempt with a new board now in place and Hamann being named new boss.
Ray Mathias had initially been told he would be kept on as manager but County have now turned to Hamann, who was part of Liverpool's 2005 Champions League-winning team.
The 37-year-old still lives in the area after leaving Manchester City in 2009.
The 62-cap international then had a year away from football before returning in a player-coach role with MK Dons last season.
The former Bayern Munich and Newcastle midfielder made 12 appearances for the League One club before finishing the campaign as Leicester's first-team coach under his former Man City boss Sven-Goran Eriksson.
Hamann must now turn his attention to putting a squad together and although he said he is unlikely to play for County himself next season, he refused to rule it out.
"With the situation as it is - only seven or eight players on the books - I've got a chance to bring in eight or nine players that I want and I think that's a big advantage," he told Sky Sports News.
"There's no rights or wrongs and I look forward to the challenge. I'll go to places I've not been before but I'm not afraid of that because that's what it's all about in football - taking up new challenges.
"Where there's a chance there's a risk, but I'll try my best to make the club successful again and bring it back to where it belongs."
Hamann added that Mathias could remain at the club while former Liverpool team-mate Robbie Fowler has been linked with a role among his backroom team.
Hamann's first competitive assignment will be a trip to Forest Green for County's Blue Square Premier opener on August 13.