Sculpted in record time -- just over two months -- after the museum was wrong-footed by Trump's shock victory over Hillary Clinton, the wax likeness stands next to one of German leader Angela Merkel and at arm's length from Vladimir Putin of Russia.
The museum was so certain that Clinton would win the November election that it decided to forgo the trouble of sculpting statues for both candidates.
"We should have had both ready, to be safe," said sculptor Eric Saint Chaffray. "So we were under time pressure," he told AFP, adding that he worked from photos and videos.
"Luckily he has sharp features that are easily caricatured. That's an advantage for us," said Chaffray, who has been sculpting US presidents for more than 20 years at the Grevin.
"He has very long hair, and it's done in a sort of wave," Chaffray told AFP. "I think he spends a lot of time on his hair every day, and he may need a simpler style once he takes office."
As with all the museum's waxworks, the Trump hair is natural and can be re-dyed as needed.
Chaffray said he thought that once he was in office, the 70-year-old Trump would tone down his hair colour, noting: "Already it's less orange, more platinum."
The work on Clinton's likeness had advanced to the stage of the modelling, said Veronique Berecz, the Grevin's press attache, adding that the museum would hold on to the work "just in case".
As for the outgoing US president, "we are keeping on Obama with pleasure," Berecz said, noting that he would take his place among other Nobel Peace laureates.
A similar Trump waxwork was unveiled on Wednesday at Madame Tussauds museum in London, complete with his signature suntan -- and yak hair.
Grevin, which attracts some 800,000 visitors a year, was started in 1882.
