The 30-year-old Portuguese, signed on a free transfer from Charlton in 2011, wants to finish his career at Hillsborough after committing himself to a fifth season.
“I couldn’t be happier because this is my home, this is my club,” he told the club’s official website.
“It’s a dream come true and I would like to finish my career with Sheffield Wednesday.
“I cannot wait to get back into the pre-season training and start the hard work for the new season.
“My confidence is high, I am feeling great and I want to continue to grow as a player here with my club.”
Semedo, who progressed through Sporting Lisbon’s youth system and had a loan spell at Cagliari before joining Charlton in 2007, has made a total of 140 appearances for Wednesday.
The club is expected to announce a new management team this week with fellow Portuguese Carlos Carvalhal understood to be poised to become general manager.
Semedo added: “There have been some changes over the summer but I know our supporters will be totally behind the whole team we have in place for next season.
“You see, these are very special supporters. We are all as one at Sheffield Wednesday, which is why I love to be at this club.”