He was most recently a first team coach at Northern Premier League high-flyers Warrington Rylands and was also an assistant at Buxton, Curzon Ashton and Colne before then.
Crossley arrives with the Greens side currently 18th in the Pitching In NPL West Division, two points clear of the relegation zone.
He replaces joint-managers Paul Bowyer and Wayne Goodison, who left the club last month after six years in charge.
The Greens have lost the last five successive matches, and their new manager will take charge for the first time in a crucial trip to bottom-of-the-table Hednesford Town on Saturday.
Chairman Stephen Richardson said: "It is a pleasure to welcome Damian to 1874 Northwich FC. We felt that his ambition to succeed, aligned with undoubted experience and understanding of the ethos and values of 1874 Northwich FC, complimented his appointment.
"As a board and a club, we look forward to working closely with Damian in the future.
"The Club would like to place on record our appreciation and thanks to the considerable number of applicants for the position of manager, and to our senior players Matt Woolley and Mark Jones who have guided the team superbly during this transitional period."
Photo credit: 1874 Northwich