Lowe joined the Owls from Bury for an undisclosed six-figure fee in September after firing 28 goals during the previous campaign and seven in as many matches for the Shakers this season.
The 33-year-old, who scored nine times in 30 appearances for Wednesday, told the club's official website: "It was very emotional and it's one of those seasons that you wish for.
"My main aim when I came to this club was to get promoted to the Championship. If it would have been any other club in League One I may not have made the move, but considering it was Sheffield Wednesday, it was an easy decision to make."
Lowe added: "A few people have had to remind me that I've had two promotions in two successful seasons. Playing a big part in two promotions is something that will live with you for the rest of your life.
"Over 38,000 fans at Hillsborough on the last day of the season was unbelievable and that day will live with me forever."