The 25 year-old is initially with the Millers until the January transfer window and hopes to draw on his experience with Stockport previously as he achieved promotion three years ago.
Logan also says he turned down other offers for the chance to work with an ambitious manager and goalkeeping coach Andy Dibble.
“We had a very good, young squad at Stockport,” he said to the Star. “I would like to think I know what this league is about and what it takes to get out of it and hopefully I can do that here.
“It is important for me to get out and play games. Rotherham are very ambitious and so is the manager. I have been very impressed with the manager. He is trying to do everything the proper way. He seems very ambitious and all the talk is about getting promoted. I am looking forward to working with him.
"I had offers from elsewhere but the chance to work with Andy Dibble who had a great career was a big factor."
However boss Andy Scott says a deal to keep Logan any longer would likely be a season long loan extension with parent club Leicester rating him very highly.
Scott said: "They see big things for Conrad. Hopefully we can push the loan on and take it until the end of the season.
"He went to Bristol Rovers last year and nearly kept them up so he will come in and add more competition."