Hill is leaving the Yeltz following six years at the helm – but will oversee the next two games while a successor is sought.
Fans called for Hill, who led the club to promotion from the Northern League Division One South in 2014, to go after Tuesday’s 2-0 defeat to Barwell. Assistant Matt Clarke is also departing.
Kitching, who has also managed Rushall Olympic, left Rangers at the end of last season, after leading them to glory in the Staffordshire Senior Cup.
Halesowen want an experienced manager who can take them to the next level.