The 27-year-old, who came through the ranks at Kenilworth Road as a teenager, still had a year left on his contract at Oakwell, but with the Tykes relegated to League One, the Hatters swooped, bringing him home for an undisclosed sum.
Immediately after Town’s play-off semi-final defeat at Huddersfield Town last month, Jones vowed to make his squad even stronger and the club are certainly keeping their end of the bargain, with the additions of Stoke midfielder Alfie Doughty and now Woodrow, both for fees.
The Luton chief said: “I asked the board and Gary this year to be bold.
"If we want to improve on last year’s position, we had to improve significantly, so we gave them a list of signings.
“Cauley is a real standout signing for us – a marquee signing.
"I’ve worked with him briefly before with England U21s and he’s a player we know really well from his Barnsley days, plus he’s a local lad as well.
“It’s a fantastic signing and I thank the board for being bold, brave and for backing me on this.
"We are sure that Cauley has the quality to make us better.
“He'll be desperate to do well because he’s that type of character.
"He’s a player with real good technical ability, he gives us good options in the attacking area and he’s a type of player that we haven’t got, a really clever player.
“It is a position that we wanted to strengthen because we know we have pace, power and athleticism.
"What we needed to add now was real quality, and Cauley brings that.”