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United are entitled to a transfer fee from the Tykes for Hayes due to his age, with a tribunal setting a price if neccesary.
Hayes has penned a two-year deal.
Iron boss Brian Laws told the Scunthorpe Telegraph: "He is not going to be here next season, that is disappointing.
"But I'm not going to blame the lad if he can get more money for himself somewhere else."
Hayes insists he was happy to leave Glanford Park.
The 20-goal striker said: "It was not a difficult decision at all to leave Scunthorpe as soon as I knew Barnsley were in for me.
"Barnsley are a bigger club than Scunthorpe and have the opportunity to push on and achieve something next season."
Kell has signed a short-term pre-contract of four months to try and prove his fitness at Oakwell, with a view to signing a two-year deal later this year.
Barnsley agreed a pre-contract with Kell on Friday April 29, the day before Kell broke his leg in a 4-0 home win over Bristol Rovers.
Kell said: "I did not think twice about coming to Barnsley. There were things that happened at Scunthorpe last season that I didnt agree with and my mind was always made up to leave this summer.
"I have come to a bigger and better club."
Tykes Andy Ritchie was delighted with the signings. He said: "Paul's signing really speaks for itself. He is a proven goalscorer, a young lad and he is going to be an excellent player.
"I am sure that he will be able to reproduce the kind of form he showed last season and will be a big part of our promotion push next season.
"Richard is a tremendous midfield player at both ends of the field and we cannot wait until he is fit enough to pull on a Barnsley shirt.
"We have had all three players watched time and time again through the season and we have been impressed by all the reports back.
"That is why we have made our moves and we are all delighted that we have been able to bring them to Oakwell".
Laws insists he is already close to securing a replacement for Hayes - with a deal offered to an experienced player who was plying his trade in the Championship last season.