The former boss of the agency has resigned "on health grounds with immediate" effect, Welcome to Yorkshire said in a statement tonight (Friday).
The agency was responsible for organising the Tour de France's 2014 Grand Depart in Yorkshire and its subsequent legacy race, the Tour de Yorkshire.
It comes after concerns were raised in relation to Sir Gary "behaviour towards staff and his expenses", the statement added.
But it said the resignation was not directly linked to the concerns raised.
Sir Gary has agreed to voluntarily reimburse Welcome to Yorkshire for "monies owed", the statement said.
In his own statement, Sir Gary apologised and asked for "time and space to heal".
He said: “Over the last ten and a half years I have always tried to set the highest standards of personal performance and leadership. Where this has been achieved, I am grateful andwhen, on occasions, I have fallen short, I apologise.
"My health is now my main priority. I ask for time and space to heal. It has been an honour and a privilege to lead such an inspirational organisation and work with sucha creative and talented team.“I know that Welcome to Yorkshire will continue to go from strength to strength and achieve manyfantastic things over the coming years.”
Welcome to Yorkshire thanked Sir Gary for his "commitment and energy" during his time at the tourism agency.
The organisation said: "Sir Gary has led the transformation of Yorkshire’s profile, most notably through the Grand Départ of the Tour de France in 2014 and the subsequent legacy of the Tour de Yorkshire, which have significantly boosted the county’s economy. We wish him well for the future.”