"I would like to place on record my gratitude to Yorkshire County Cricket Club for allowing me to coach in the Big Bash League," Gillespie said in a statement.
"I am looking forward to bringing back some knowledge and experiences to Yorkshire, which will improve our T20 cricket going forward."
Former Yorkshire chairman Colin Graves' appointment as England and Wales Cricket Board chairman fuelled speculation that Gillespie might succeed Moores, who has been under fire since England's meek exit from the World Cup.
In his second stint as England coach, Moores has held on to his role and is touring the Caribbean where the test side are playing West Indies.
(Reporting by Ian Ransom; editing by Greg Stutchbury)
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