The artwork, done electronically, features Mr Hockney’s interpretation of the London Underground logo.
It caused a backlash from London artists when it was unveiled earlier this month.
Artist Laura Nevill called the drawing “a missed opportunity” from Sadiq Khan to showcase upcoming artists in prominent landmarks as part of his #LetsDoLondon campaign to encourage cultural recovery in the capital.
But speaking to the Yorkshire Post on a visit to the region yesterday, the Mayor defended the use of the picture, which Mr Hockney donated to Transport for London.
Mr Khan said: “One of the great things about being mayor of London is all the great partnerships with other regions.
“I love Yorkshire and David Hockney one of your proud sons. He is respected around the world for his art and he very kindly gifted us the piece of art.
“He’s not just one of Yorkshire’s proud sons but one of the country’s proud sons.
“The great thing about art is that it’s a conversation starter. This piece of art has got people talking.
“He’s helping us bring tourists back. There’s nothing wrong with a bit of controversy.”
Mr Khan said an exhibition showcasing Mr Hockney’s work at the Royal Academy was intrinsic to London’s cultural recovery.
The exhibition, David Hockney: The Arrival of Spring, features 116 new works by Mr Hockney created on his iPad during the first wave of the pandemic.
They were created in Normandy, where the artist spent the first lockdown.
Tickets to the exhibition, which opens on Sunday, have already sold out.
Mr Khan said: “We couldn’t get tourists or Londoners going to the Royal Academy if it wasn’t for David Hockney. Once again, Yorkshire is helping London.”
The Mayor made the remarks on a visit to Switch Mobility in Sherburn-in-Elmet to see how the factory produces electric buses that form part of the London fleet.
He was joined by the new Mayor of West Yorkshire, Tracy Brabin, who was elected earlier this month.