The Liverpool-born player spent a brief loan spell with United back in 2013 as a 21-year-old.
Now 30, Eaves, whose signing followed on from the capture of Luton Town wing-back Peter Kioso, said: “I am a different animal to what I was at that age and I am looking forward to getting going.
“My mentality (has changed) absolutely, 100 per cent. I just think that back then, I always gave 100 per cent.
“But now, it is just working a lot smarter and knowing the areas I need to be in and just being the most efficient number nine I can be.
“But make no bones about it, it is goals that I am going to be interested in this year when I see the ball coming in from both sides.”
A physical presence and focal point up front with a strong work rate, Eaves feels his all-round game makes him a natural fit for the club under Paul Warne as well.
Eaves, who scored 18 goals in 107 appearances for Hull, continued: “Stylistically, I felt like Rotherham would really suit me.
“When he (Warne) spoke to me, he spoke about the style of play and how we want to play and I just feel like I will be a really good fit for this team.
“I’d like to think I will be a good addition to the lads.
“It’s a really tough league and you have strong teams coming down and big clubs coming up.
“It will be a challenge, but I can see from meeting everyone that we are a really strong, honest group of lads and I am looking forward to working with every one of them.”