Tony Daws, Andy Crosby and Ian Baraclough will act as his assistants, with Adkins handed a one-year deal.
"Before joining Scunthorpe he enjoyed much success with Bangor as their manager, twice winning the League of Wales, which took them into the European Cup, and also managed the League of Wales National Representative team - again enjoying a successful two-year term of office," Iron chairman Steve Wharton told the club's website.
"I am sure everyone associated with our football club will give Nigel and his management team their full support as we progress towards our aim of Championship football."