The 31-year-old has joined for an undisclosed fee, penning a three-year deal, but the transfer was not finalised in time for tonight’s clash at Burton Albion.
He becomes Wednesday’s sixth summer signing, following in the footsteps of Steven Fletcher, Jake Kean, Daniel Pudil, Almen Abdi and Will Buckley.
Jones only signed a new two-year contract at Turf Moor last summer but it is thought Wednesday recently triggered a buyout clause in his deal.
In an interview with the Daily Mail, Jones said: “It was a bit of a whirlwind few hours to be honest. When I arrived at training yesterday I had a message on my phone from my agent saying that Sheffield Wednesday have matched the buyout clause in my contract and that I can go for a medical in Sheffield.
“So I drove over to Hillsborough from Burnley and a few hours later I had completed my medical and everything had been agreed, so I was able to sign the contract.”
Jones, who came through the ranks at Premier League giants Manchester United, joined Burnley in 2013 following his release from Wigan Athletic.
He has four promotions to the Premier League on his CV, including two with the Clarets.
“Wednesday is a massive club with fantastic, passionate fans and I’m delighted to be here,” said Jones. “I can’t wait to get started. I supported them growing up and loved watching the likes of Chris Waddle play.”
Jones featured 43 times in the 2015/16 campaign as Burnley went up at the first time of asking, with his only goal coming in their home win over the Owls.
The central midfielder, previously of Derby County and Wolves, started the Clarets’ top-flight opener last weekend. He was taken off with three minutes remaining of their home defeat to Swansea City.
Jones said he enjoyed his three years at Burnley but is looking forward to a new chapter in his career.
He is regarded as a good passer and will give Wednesday another useful option from set pieces.