Rowing, 70, will step down at the end of the month, ending nine years in the role of general manager, director and then chief executive.
The Tykes survived another season in the npower Championship with a last-day draw at Huddersfield following the heroics of their management team of David Flitcroft, Micky Mellon and Martin Scott, while the club announced the appointment of former Manchester United director Maurice Watkins as their new chairman last week.
Rowing, who also confirmed a new chief executive will soon be in place - reported to be Ben Mansford, director at sports agency Wasserman Media Group - told Press Association Sport: "The new guy will take over from myself as chief executive and Maurice will head the board as chairman.
"We've been without a chairman for five years, so it's all change here at Oakwell and I'll leave the club on very good terms and in a good state in terms of the financial situation.
"I've enjoyed a very good relationship with the vast majority of fans and of course I will miss that and the day-to-day dealings with people at the club."
Rowing added: "There are some exciting times ahead for the club. The game on the last day at Huddersfield was a tremendous occasion where both clubs showed true Yorkshire spirit.
"We stayed up by the skin of our teeth and now we can have another crack at it next year. I think fans can look forward with optimism.
"We've said in the past that just to stay in the division would represent success and I think we've put too much on that.
"Now we need to push on from there and all the changes hopefully will provide the foundations for us to start looking towards the top seven or eight."