The 40-year-old has agreed a deal until the end of 2018-19.
BBC Radio Leeds reports the Whites paid £500,000 to activate a release clause in Heckingbottom's Barnsley contract, which he only signed on Friday.
A Barnsley statement declared their "thorough disappointment" at Heckingbottom's departure.
"The club are shocked at Paul Heckingbottom's desire to leave, having agreed a new contract last week following the completion of the transfer window, where the directors worked tirelessly along with Paul to secure their targets, resulting in a successful window," the statement said.
"This left the club optimistic in a turnaround in form and a strong end to the 2017-18 campaign as we battle to retain our position in the league.
"Until a new head coach is appointed, Paul Harsley will take caretaker charge. The board fully trusts him to lead the team."