Robins, 39, leaves Rotherham United and brings backroom members John Breckin, Nick Daws and Steve Taylor to Oakwell with him.
The ex-Man United striker was expected to be unveiled on Monday but problems with a compensation package meant the move had to be delayed but the two clubs agreed last night.
Robins told Barnsley Player:
"I am delighted to be here after a protracted few days and I can now start the job. It has been frustrating and I have been kept waiting in the wings a little but at the same time thankful that it has all be sorted out and resolved. Barnsley FC have given me a tremendous opportunity.
"I had been at Rotherham for nine years as a player, youth team coach and manager and spent a large proportion of my working life there. The club will hold a place close to me for a long, long time and we had some good times there. It has been a turbulent time but I am looking forward to the new challenge.
"I know one or two of the squad here from my playing days and I am really looking forward to working with them. Hopefully we can hit the ground running. There is a clean slate for everyone. What has happened in the past does not make any difference and as a new manager coming in I have my own ideas. I have my own coaching staff and we are looking forward to getting started, seeing what they can do and what they are capable of.
"We have to get points on the board quickly. We are playing catch up and our season starts now".
He added: "I need time to stamp my authority on the team and that is something I have done in the past and I am not adverse to doing that. In football you have to be able to adapt and you are dictated to a little by the players you have available.
"You have to try and get the best out of your players and put them into the positions they are most suited to. I am not going to try and reinvent the wheel and it is important that we pick up points as quickly as possible.
"This is a job I am relishing and looking forward to".