"The board has investigated (allegations) and concluded that Sir Gary made errors of judgement regarding his expenses at a very difficult time for him and his family," Welcome to Yorkshire said in a statement.
"Sir Gary has agreed to voluntarily reimburse Welcome to Yorkshire for monies owed."
The agency said Verity, who had been their chief executive since 2008, was resigning on "health grounds".
"My health is now my main priority. I ask for time and space to heal," Verity said.
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The fifth edition of the Tour de Yorkshire is being held from May 2-5 this year.
(Reporting by Rohith Nair in Bengaluru; editing by Clare Fallon)
