Earlier this week, Heckingbottom made the decision to accept an 18-month contract at Leeds, despite having just penned a new deal at Oakwell.
However, while acknowledging the criticism which he has received, Heckingbottom has said that he remains "comfortable" with his decision.
In a statement, Heckingbottom said: "I understand the anger of many supporters because of the speed and location of my next job but I have never made a secret of the fact that I am ambitious and would leave at some point to further my career.
"As I have said before, one of the reasons I took months to consider signing my first contract as Barnsley head coach was because I was, in one way or another, going down a path that would see me leave the club.
"Sometimes the time to leave naturally becomes apparent. We are not always able to chose when opportunities will arise. Sometimes you just have to take them. I am comfortable with my decision and I am looking forward to a totally different challenge."
Heckingbottom joins Leeds with the club sitting seven points adrift of a playoff spot in the second-tier standings.