Cosgrove, 26, was a free agent after being released by Birmingham City and scored eight goals in 33 third tier appearances for Plymouth last season.
The 20-year-old ended last season on loan at Rochdale and made 18 appearances in League Two.
The Tykes have taken seven points from their first five games this season.
The Sky Blues have secured the 23-year-old centre-back for an ‘undisclosed’ fee – understood to be in excess of £4m with add-ons – with the Tyles’ skipper putting pen to paper on a four-year deal at the CBS Arena to become the club’s 11th capture of the windowMark Robins had to work hard to get the move over the line, with the club having had two bids rejected by the League One club who appeared determined to fight to keep their highly-rated defender. City initially had a £2.5m bid, rising to £3m, rejected by the Oakwell club before going back in with a revised £4m bid. That, too, was dismissed on Thursday before City went back again for a third time.
Kitching signed for Forest Green Rovers in 2019 where he stood out and caught the eye of Barnsley, who drafted him in on a four year deal for a reported £600,000 fee in January 2021
“Liam is a talented player, who is versatile across the back line. He is a strong defender who is comfortable with the ball at his feet, and provides leadership as well and a maturity beyond his years.
“We are very pleased that he has chosen to join us and look forward to working with him.”
