Dave Jones was sacked by Wednesday last weekend after a poor run of results and the Hillsborough club were reported to be lining up Evans as a replacement.
But Evans told the club website: "I can confirm I was called to a meeting with my chairman Tony Stewart and chief operating officer Paul Douglas earlier this morning (Tuesday). The meeting was primarily to discuss a matter which relates to the recent press speculation over the last 24 hours.
"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 set for me by a very supportive chairman and board of directors."
Chairman Stewart added: "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.
"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."