Evatt, a Spireite between 2003 and 2005, has made a surprise return as a free agent having been released by Blackpool at the end of last season.
The 31-year-old centre-half has signed a two-year deal at the Proact Stadium and believes it might not be too long before he is back playing in the second tier with the Derbyshire club.
"People will probably raise a few eyebrows with me dropping down to League Two but at this stage of my career I have nothing to prove and money isn't my motivation, I just want to play football," said Evatt.
"I've come here to play first-team football. A fit Ian Evatt should be playing week in, week out at this level because in my opinion I'm still a top Championship player.
"My record speaks for itself. I've captained Blackpool to promotion and played in the Premier League so I don't have anything to prove.
"I turned down offers from Championship and League One teams to come to Chesterfield because this is where I want to be.
"Obviously it's home for my wife and family but I was impressed with the manager and the way he wants to play football and I was impressed with the stadium, it's much different to Saltergate when I was last here, and the club as a whole.
"I've been impressed with the chairman, he wants to get to the Championship in two years and I can see no reason why we can't do that and I want to be part of it.
"Anything other than promotion this season would be a failure. We won't take anything for granted because in football you can't, but if we work hard week in, week out then with the calibre of players that are here that is a more than realistic target."