Young, 41, replaces Lee Sinnott, who parted company with the Robins after five years in charge.
The former Chester and Colwyn Bay boss was most recently in charge of Conference North side Stockport County, but he resigned in January.
He has brought in his long-serving assistant manager Gary Jones, with whom he has worked with at three clubs.
Altrincham's relegation was confirmed on the final day of the season when they lost 3-0 at home to Braintree.
Relegated National League side Altrincham have appointed Neil Young as their new manager.