Robins, 39, has been in charge at Millmoor since March 2007 and will now speak to the Reds board about taking over as boss.
Robins' managerial record at Rotherham reads: Played 128, Won 55, Drawn 30, Lost 43, giving him a win percentage of 42.97%.
A statement on the official Rotherham United webite from chairman Tony Stewart reads:
"I believe Mark's future is here at this club and I am convinced that he will remain our manager after meeting with Barnsley. We have made tremendous strides over the past 18 months both on and off the pitch and needless to say Mark has been an integral part of the progress we have made. Nevertheless from the moment I took control of the club I have said I would never stand in the way of anyone here and this opportunity has come along for Mark. Our ambition for this club remains as resolute as ever and that is to be a Championship side in our own new stadium in Rotherham in the next three years and I am and remain totally committed to those goals".
More soon.