The Millers have appointed the Crawley Town chief, 49, as Andy Scott’s successor after an exhaustive interview process.
Evans, who has led the Sussex club to within touching distance of League One just a year after winning promotion to the Football League, impressed the United board and will officially take charge today.
A compensation package is understood to have been thrashed out over the weekend between the two clubs before Evans signed a three-year deal.
Stewart last night told the Yorkshire Post: “We had a lot of applicants and were, basically, spoilt for choice. I am sure that is down to us moving into the new stadium this summer.
“The quality of candidate that we saw was very high but Steve really stood out. He is the man of the moment after taking Crawley into the League and then ensuring they are in the mix for automatic promotion even after losing his two main strikers.
“He has the drive and passion that we feel matches our own. His drive is what has taken Crawley so far and I see him as the perfect fit for Rotherham at what is an exciting time in our history.
“Steve has real drive about him. As a club, we have felt ready to take off for a couple of years but we have just missed out.
“But that determination and passion burns as brightly as ever and in Steve we have a manager who we believe can move us forward.”
Evans, who will be joined at the Don Valley Stadium by assistant Paul Raynor, has been in charge of Crawley since 2007 and led the club to the BlueSquare Premier title last season.
They led the way in League Two earlier in the season but slipped out of the automatic promotion places after selling top scorers Matt Tubbs and Tyrone Barnett.
His most recent visit to Yorkshire ended in controversy when his Crawley side were involved in an ugly brawl after beating Bradford City 2-1 at Valley Parade a fortnight ago.
The rumpus saw five players red-carded on the night and another subsequently banned for three games after the FA studied video evidence. Both Crawley and Bradford will learn their fate tomorrow after being charged over the incident.
Fingers were pointed at Evans and assistant Raynor from within the Bantams’ camp as to how their touchline antics had led to tempers boiling over in such a spectacular fashion after the final whistle.
But Stewart said: “What you see on a match-day is very different to what you see away from the pitch. We are happy to have appointed the man we wanted.”
On the conclusion of United’s search for a new manager, Stewart added: “His name kept coming up in discussion so we approached the Crawley chairman for permission to speak to Steve.
“Their chairman was superb in the discussions and the paperwork was completed on Sunday night, ready to make the announcement ahead of the Cheltenham game.”