Assistant coach Frank Barlow has also left the League One club as Chris Morgan takes charge of the side for the rest of the season.
United are currently in the playoff places, despite Tuesday's 2-0 defeat at home to Crawley Town.
Wilson joined the Blades in June 2011 following a three-year spell with Swindon Town.
"We must thank Danny and Frank for all their endeavours and hard work over the past two seasons," United owner Kevin McCabe told the club's official website.
"We now have a mini season for this club to achieve success and we will all back Chris in this mission."
The team returns to action on Saturday when they welcome promotion rivals Swindon to Bramall Lane.