The The 26-year-old striker left Middlesbrough to spend the remainder of the season with the Owls, with the view to a permanent transfer.
Rhodes only joined Boro from Blackburn Rovers for around £10million on deadline day last year but after making just six appearances under Aitor Karanka this season, has no regrets leaving Teesside for a Championship return.
"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 just love playing football in whatever league. I've played in all of them now, I loved playing in the Premier League as much as I loved playing in the Conference.
"There's no better feeling than waking up on a Saturday and having that anticipation of what might come from the day.
"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."