The Barnsley defender is set to be reunited with his former Oakwell manager after agreeing a two-year deal at Easter Road.
It was Heckingbottom who signed Jackson when the centre-back chose to leave Middlesbrough in 2016, and the 25-year-old is looking forward to working alongside his old mentor again.
Jackson, who visited Easter Road last month to see his new side in action against Edinburgh rivals Hearts, told the club’s website: “I’m delighted to be joining Hibernian.
“With the stature of the club and having worked with Paul previously it was a no-brainer for me. I know what he expects of me and I know what I can deliver for him.
“I obviously got a glimpse of what to expect when I was up for the game against Hearts and I’m looking forward to experiencing it all myself when I report back with the rest of the boys in three weeks.”
Former England youth international Jackson becomes Hibs’ second signing of the summer, following the return of Scott Allan, with Heckingbottom believing he is tough enough to deal with the Scottish game.
He said: “I’m really pleased we have been able to get the deal for Adam over the line.
“The fact it’s come so early in the summer is hopefully indicative of the work that has gone on, and is going on behind the scenes here. It also shows Adam’s own enthusiasm to play for Hibernian.
“I know all about Adam’s qualities having signed him in the first place for Barnsley, and he was one I was set on bringing to Easter Road.
“Adam initially caught my eye when he excelled at a young age in League Two while on loan with Hartlepool United, and I watched him for a long time before signing him for Barnsley.
“Adam has a real physical presence. He is strong in the air and understands how we want to defend and how we look to play out from the back. So, he’s ideally suited to the way we like to play.
“He got a taste of what it’s like when he was up to watch the last Edinburgh derby and I know how excited he is to get going with the rest of the boys when we start back for pre-season training.”