The 48-year-old former Everton defender joins with the Latics 14th in the Vanarama National League.
Club legend John Sheridan ended his sixth spell at the club on Saturday – bowing out with a 3-2 comeback win against Eastleigh.
Speaking following his appointment Unsworth said: “This is the perfect job for me and I’m hugely excited to be joining the club at this time.
“I’ve had opportunities to become a first-team manager at a number of clubs over the past three of four years but they haven’t felt quite right.
“This is the right club, the right fit, with the right owners and board of directors.
“The fanbase has also been a very important factor in my decision to join. I’ve seen the support they have given the team this season and I’m sure they’ll continue to get right behind the team.
“I genuinely think this club is a sleeping giant, one that can climb up not just one league, but two or three, in a short space of time.
“I’m very pleased to be here and I can’t wait to meet the players and get started in the job.”