The Millers, who were last promoted in 2000/01, ended a six-year stay in League Two by claiming second spot after their campaign ended with five successive wins.
And Stewart, who brought the Millers back to Rotherham last summer after a four-year stay in Sheffield, is looking to go straight through League One and return to the Championship.
"We are in it to win it. I don't see any difference between League One and League Two," he told Press Association Sport.
"Yes, there will be better competition but we will go for it and my ambition is to win promotion at the first attempt.
"The opportunity to have the derbies and playing teams like Wolves is exciting. But when Steve (Evans) brought in the players he did we said it wasn't going to just be a League Two team, it was going to be a League One to Championship side that could hit the ground running.
"There will be a little tweaking. The manager is talking about one or two players but we have got the basis of a good team going into League One."
Evans was appointed into the Millers' hot-seat last April and became Stewart's fourth managerial appointment in four years. There were plenty of eyebrows raised when it was announced, but the chairman feels vindicated after the Scot delivered a third successive promotion.
"The reason I brought Steve in was because what we wanted was a manager that could get promotion," he added. "I looked at his CV and it told me this guy was a winner and he's proved that this is the case."
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