The Millers ended their six-year exile from the third tier when they beat Aldershot to register a second-placed finish in League Two on Saturday.
Chairman Tony Stewart has already expressed his desire for another promotion push next season and Evans believes he has a capable squad.
"We are very proud to be going into League One," he said. "Our planning will be meticulous and I have always believed when we have our best players on the pitch we will win football matches.
"This group can all play at that level without blinking. I had to work very hard to persuade a lot of these players to come to League Two. I asked them to believe in me and what we were trying to do.
"If you look at who we signed, we have four or five players who could play in the Championship. Championship teams have already bid for three of them."