Berylson was made chairman at the Den in March 2007 and half a year later he axed manager Willie Donachie with the Lions struggling at the bottom of League One. For his first managerial appointment, the American businessman turned to then Manchester City reserve-team boss Jackett, and it sparked the start of a long-lasting working partnership.
"On behalf of the board of Millwall Football Club, I want to express my thanks to Kenny for his fantastic service and achievements over the past five-and-a-half years," he told the club's official website.
"He has played a major role in creating a stable environment at Millwall which hadn't been the case prior to his arrival.
"On a personal level, whilst respecting Kenny's decision, I wish I could have persuaded him to change his mind. He was my first acquisition as chairman of the club and has proved himself to be one of the best."
Jackett kept Millwall up in his first year in charge before they reached the play-offs the following year, but they were beaten by Scunthorpe in the final at Wembley.
But in 2009/10, the Lions returned to the iconic stadium to face Swindon, after seeing off Huddersfield in the semi-finals, and they were promoted thanks to a 1-0 win.
They have remained in England's second tier since, though a disastrous run of four defeats in their last five games this season saw them come perilously close to dropping back into League One, despite Jackett leading his men to the FA Cup semi-finals.
It led the manager to decide to call time on his spell with the club, much to the despair of his chairman.
"I am losing a great manager, but he will remain a good friend and hopefully, golf partner," Berylson added. "I know everyone associated with Millwall, management, staff, players and fans, will wish Kenny all the very best with his future endeavours, except for those times when he might oppose us on the pitch."