A source close to the situation said the 33-year-old Spiker and Army athletic director Kevin Anderson agreed on the terms of a deal late Thursday as Spiker was finishing up his on-campus interview.
Anderson fired Crews last month after what Anderson termed an "overreaching incident."
Spiker has been instrumental during his five years under Steve Donahue in the revival of Cornell basketball. The Big Red have gone 50-20 recently in the Ivy, won the past two league championships, been to the NCAA tournament two years in a row and are the conference favorite yet again this season.
Spiker wasn't on Anderson's original interview list last week in Chicago, but Donahue called Anderson and let him know that Spiker was in Chicago recruiting, according to a source.
Anderson had said he was looking for a fresh face, someone who could motivate young cadets the way the late Maggie Dixon did with the women's team. Dixon was a DePaul assistant when she was hired and led the Black Knights to an improbable Patriot League title and NCAA tournament berth in her one season in 2005-06. Dixon died of a heart condition on April 6, 2006.
Like Dixon, Spiker never served in the military or coached at a military academy.
Spiker is expected to retain the three current assistants on the staff. Anderson said last week Army would honor their contracts.
Andy Katz is a senior writer at ESPN.com. Information from The Associated Press was used in this report.