Warnock was appointed on a short-term contract on Thursday, three days after Neil Redfearn's dismissal.
Kevin Blackwell, who has worked with Warnock since 1986, will join him at Rotherham as assistant coach.
"This is the 14th time I've retired and my 15th comeback, but I do enjoy it," Warnock told BBC Radio Sheffield.
"I didn't expect to be here this time last week, but that's football. I've never been a manager just to do things for the sake of it.
"I was probably the best bet for them - my wife hasn't been so well but she told me to go for it, and that's what I'm going to do."
Rotherham are 22nd in the table and without a win in five games, and Warnock's primary task is to save them from relegation.
"I'm only here for 12 weeks and I'm not going to change everything in 12 weeks. I need to get results as soon as possible," he said.
"I think when I finish football, the fans will remember that when I've left a club, I don't think I leave them in worse-off situations.
"They all have memories of what I've done and enjoyment, and that's what football is about, not falling asleep watching your team play."
The 67-year-old has been without a managerial role since December, when he left Queens Park Rangers after a spell as temporary boss.
"We know it is going to be difficult, but there will be some players at Rotherham now who will really give me satisfaction," he added.
"They are a genuine bunch - there's no bad eggs as far as I can see. The club is the most important thing and we all have to be singing off the same hymn sheet."
Rotherham United manager Neil Warnock said he does not leave clubs "in worse-off situations" after taking charge until the end of the season.