The Owls are thought to have requested permission to speak with Evans, who has steered Rotherham to the Sky Bet League One play-off places following promotion last season, after sacking Dave Jones at the weekend.
However, Stewart is adamant the Glaswegian will be remaining at the New York Stadium.
''Despite the recent press speculation over the past 24 hours, I would like to fully clarify that Steve Evans will not be joining Sheffield Wednesday,'' said Stewart in a statement released by the club.
''Steve is a key part of Rotherham United's efforts to progress to the Championship and both the board of directors and Steve are delighted with progress made so far.
''We will now draw a line under the speculation as we look to prepare for the FA Cup second-round match with Rochdale this Saturday.''
Following on from his chairman, Evans also ruled himself out of the running for the job at Hillsborough and insisted it was business as usual.
''I can confirm I was called to a meeting with my chairman and chief operating officer Paul Douglas,'' Evans told the club's official website.
''The meeting was primarily to discuss a matter which relates to the recent press speculation.
''In that said meeting I reiterated my commitment to Rotherham United FC and the project I started some 18 months ago.
''As a manager you must remain focused on the job in hand and there is certainly much work to be done not only immediately but also in the medium and long term.
''When your team is winning football matches on a regular basis and playing a brand of football that is exciting to watch, there normally follows an admiration for what you are delivering.
''However, I will not allow anything to take my focus off the work that is needed to deliver the objections [sic] set for me by a very supportive chairman and board of directors.''
Wednesday chairman Milan Mandaric is currently drawing up a list of potential candidates.
Former Leeds and Sheffield United manager Neil Warnock is rumoured to be in his thoughts, and the 65-year-old is willing to do a short-term job until the end of the season.
Mandaric plans to start the interview process this week, although the chances of appointing a new boss before Saturday's visit of Nottingham Forest look slim.
Wednesday gave their Championship survival hopes a boost on Tuesday night with a 2-1 home win over Leicester in Stuart Gray's first game in temporary charge.