The 23-year-old, who had been at Elland Road since the age of eight, has signed a three-year deal after Wednesday paid an undisclosed fee.
Lees came through Leeds' youth academy before breaking into the first team and also spent time on loan at Accrington Stanley and Bury.
With 207 senior appearances under his belt, the former England under-21 international is looking forward to the fresh challenge he faces at Hillsborough.
"We've been in talks and I've been hoping everything was OK and I'm delighted to have put pen to paper," he told Wednesday's official website.
"You never know with any deal until it's signed, of course, and I couldn't be happier.
"This is a massive football club steeped in top-flight history for most of its existence and I can't wait to get started.
"I've spoken to plenty of players who have played for Sheffield Wednesday and they can't speak highly enough of the place.
"Obviously, that has a big bearing on your decision and it's great that so many people in the game speak so well of this club."
