Image: The 6m blimp depicts Mr Trump as a nappy-clad orange baby.
The protesters, who describe themselves as a group of anti-fascist art activists, said at first the mayor's office did not recognise "Trump Baby" as a legitimate protest.
"But following a huge groundswell of public support for our plan, it looks like City Hall has rediscovered its sense of humor".
"Trump Baby can become a permanent feature of this terrible Presidency, a constant, unmissable reminder of the contempt with which this embarrassment of a man is held by everyone outside of his deranged, bigoted base", the group said.
"The mayor supports the right to peaceful protest and understands that this can take many different forms", a spokesman for Khan said.
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There are restrictions in place: the dirigible can go no higher than 30 metres and will only be up from 9.30am-11.30am. The mayor's operations team met with the activists and gave them permission to use the square as a "grounding point", the outlet reports.
His representative added, "However, the organizers will also need to receive the necessary approvals from the Metropolitan Police and National Air Traffic Service in order for it to fly".
The presence of the balloon may acerbate tensions between Khan and Trump, who have been embroiled in several Twitter spats.
But he also told Channel4 News that a state visit by the U.S. President should be cancelled.
Trump is scheduled to visit London next week after much delay, with concerns over protests having scuttled previous plans.
The angry infant will take to the skies on July 13th with the support of London Mayor Sadiq Khan.