The images filmed on Saturday show a heavily built man in a black duffel coat square up to several police officers before knocking them down in a hail of punches and kicking them on the ground, AFP reported.
One of the officers is then beaten by other protesters wearing yellow vests before he is rescued by fellow riot police in protective equipment and helmets.
The ex-boxer, identified by French media as 37-year-old Christophe Dettinger, is a former heavyweight professional fighter who reportedly works for the local government in the Essonne area south of Paris.
Interior Minister Christophe Castaner said Dettinger, known in the ring as "The Gypsy From Massy", a town south of Paris, had handed himself into police in the capital.
"He was immediately arrested and will be held accountable for his acts by the justice system," Castaner added.
Around 50,000 "yellow vest" protesters took to the streets again on Saturday in cities around France to denounce the centrist government of President Emmanuel Macron, leading to clashes in Paris, Bordeaux and Rouen.
Dettinger could face years in jail if convicted over his rampage on Saturday on the Leopold-Sedar-Senghor bridge which links the Tuileries gardens to the Musee d'Orsay in central Paris.
Assaulting a police officer can lead to up to three years in prison and a fine of €45,000, though sentences can be increased in certain circumstances.
The French boxing federation issued a statement condemning the violence, saying that it "ran completely contrary to the values of our sport".
"The French Boxing Federation sends its support to the family and loved ones of the officer who was a victim of this individual, but equally to all the security forces who have been on duty these last weeks," it said.
Dettinger's former coach, Jacky Trompesauce, had urged the father of three to give himself up to police earlier on Monday.
"There was something that set it off, which I learned overnight," Trompesauce told RMC radio on Monday morning, claiming that a woman was attacked by the police, prompting Dettinger to respond with a flurry of punches.
"Yellow vest" protests against fuel taxes began in rural and small-town France in late November, but then mushroomed into a wider revolt during December against the policies and governing style of 41-year-old Macron.