The historic monument has been adorned with 25,000 square metres of silvery-blue fabric and 3000 metres of red rope.
Neither Christo nor Jeanne-Claude lived to see its completion.
Jeanne-Claude died in 2009, and Christo died in 2020, after a long career in which the couple wrapped iconic buildings around the world including the Reichstag in Berlin and the Pont Neuf in Paris.
Before his death, Christo had already completed the plans for the Arc de Triomphe, which was originally scheduled to take place in autumn last year.
But following the artist's death at 84 and due to the coronavirus pandemic, the project had to be postponed.
The costs for the wrapping, around 14 million euros ($A23 million), were financed by Christo himself - among other things through the sale of sketches, collages and plans.
More than 1000 workers, engineers and climbers worked on the project, the idea for which dates back to the 1960s.
The work can be seen until October 3.
AAP with The Project.