Mr Trump is due to meet Theresa May at 10 Downing Street on 13 July.
Campaigners raised almost £18,000 for the helium-filled six-metre high figure, which they said reflects Mr Trump's character as an "angry baby with a fragile ego and tiny hands".
London Mayor Sadiq Khan gave permission for the balloon to fly.
The White House has been approached for comment.
On Twitter former UKIP leader Nigel Farage said the plan was "the biggest insult to a sitting US President ever".
Under the plans the inflatable will be allowed to fly for two hours on the morning of Friday 13 July.
Leo Murray, who is behind the crowdfunded idea, said: "[Mr Trump] really seems to hate it when people make fun of him.
"So when he visits the UK on Friday, we want to make sure he knows that all of Britain is looking down on him and laughing at him.
"That's why a group of us have chipped in and raised enough money to have a six-metre high blimp made by a professional inflatables company, to be flown in the skies over Parliament Square during Trump's visit."
More than 10,000 people signed a petition calling for the inflatable to be given permission to fly, activists said.
Mr Khan and Mr Trump have repeatedly clashed on Twitter, including in the aftermath of the London Bridge attack.
Before the figure can take off, campaigners will also need permission from the National Air Traffic Service (NATS) as the project constitutes a "non-standard flight in controlled airspace", a spokesperson said.
Because Parliament Square sits within restricted airspace, additional approvals are also needed from the Metropolitan Police.
Max Wakefield, who is one of the people working on the project, said the group is "confident it will obtain all necessary permits".
He said the initial crowdfunding target was just £1,000, but this was reached within 24 hours.
The extra cash will now be used to send the balloon on a "world tour" and "haunt" Mr Trump wherever he goes, he added.
The Met has been approached for a comment.