Bennett, also the current England coach, meanwhile replaces Seibold in South Sydney bringing forward the swap a year early.
Bennett will return to Brisbane in round eight next season as coach of the Rabbitohs.
"We were certainly disappointed with the way that played out," White said.
"Today's decision has certainly not been easy. It's a very tough decision, one we never saw coming. We no longer had faith that we could give ourselves the best chance of performing if we continued on the path we were continuing on."
Bennett first became Broncos coach for the club's inaugural season in 1988 as part of a 20-year stint which saw the club win six titles.
He then left to coach the Dragons in 2009, winning the NRL title in 2010, where he coached for three seasons before taking over the Knights for three seasons.
In 2015 he returned to Brisbane as the club made the grand final before losing a thriller to the North Queensland Cowboys.
Bennett had already signed a deal to join the Rabbitohs in 2020 on a two-year contract, which is now extended to a three-year deal, the club announced last night.
"I'm really pleased it's all resolved and that I can join this great club with a free mind, knowing I did the right thing by the fans, staff and players," Bennett said.
"It's a wonderful club, South Sydney, and I feel privileged to have the chance to coach this team."