"I feel it represents a decent opportunity for Graham, it represents our strategy in moving forward at the club as I am now looking to strengthen the team on the back of the deal.
"We are blessed at the back with players who have played in a higher division so from that point of view we are okay and I am looking to strengthen different areas, so now it gives me scope to do so.
"I want to thank Graham for what he did for us last season when he missed just one league game. We wish him all the best for the future."
The Shrws first approached Rotherham about Coughlan in January but the move petered out after a meeting in May, boss Paul Simpson said of the deal: "I'm really pleased as Graham was one of my first targets."