The Scottish striker joined the Owls on loan until the end of the season, with a view to a permanent move in the summer, after struggling to break into Aitor Karanka's side.
"Middlesbrough is a fantastic club and I really enjoyed my time there," Rhodes told Sky Sports News. "I made such great friends and it's sad that I couldn't have played the games I would have liked.
"But life moves on and football is such a short career, you have to make the most of it while you can. I'm really delighted to be part of the Sheffield Wednesday squad and I'm looking forward to getting started.
"I wish Middlesbrough all the best, but I love playing football and that [made my decision]. I'm happy to be here and hopefully will play a few more minutes and contribute to what is already a great season at Sheffield Wednesday."
Wednesday find themselves seventh in the Championship table heading into Friday night's game at Wigan Athletic.