Former Manchester United and Norwich striker Robins, 39, has impressed since being appointed Rotherham manager in 2007.
Millers chairman Tony Stewart said: "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."