The 40-year-old takes over at League Two Barrow and leaves the club fighting for a play-off place.
Whing took Moors to within a penalty shoot out of promotion last season, losing at Wembley to Bromley before FA Trophy final defeat against Gateshead.
The club's performances have not gone unnoticed and Moors now need a new manager.
“The club is naturally disappointed with Andy’s decision to leave at such a critical point in the season but we understand and respect his decision to pursue this new chapter in his career,” a statement read.
“For this reason, we granted Barrow permission to speak to Andy and we would like to thank them for the professional way in which they have conducted the negotiation.
“Andy leaves with the gratitude and best wishes of everyone at Solihull Moors and we thank him for his service to the club, especially for the memories of last season.
“Craig Pead will also be departing to join Andy’s backroom staff at Barrow”
The club added: “The board will now begin the process of appointing the new Head Coach. In the meantime, Richard Stearman, Kevin Poole and Stephen Ward will oversee training and manage upcoming fixtures, pending the new appointment.
“As supporters will know, we have been somewhat disappointed with our results and performances this season, especially given the quality of the squad.
“This unforeseen turn of events now provides the opportunity to appoint a high quality replacement who shares the club’s ambition and community ethos and can get the best out of an undoubtedly talented squad, as we seek to reach the play-offs once again.”