Robert arrived in Havana last week, and has been waiting to get authorities' permission to begin the stunt.
Cuba agreed to let him go ahead, and dozens of police were on hand Monday to keep order. In other countries, Robert has often pulled off his stunts without seeking permission, and has sometimes been arrested.
Just before the climb, Robert scoped out the building, which once was the Havana Hilton.
Though a fall would almost certainly kill him, the Frenchman said he was not intimidated.
The hotel is one of the Cuban capital's most iconic buildings, taken over after the 1959 Cuban Revolution and redubbed the "Habana Libre," or "Free Havana." Fidel Castro briefly set up his personal offices in the hotel after his triumphant march into the capital.
Associated Press writer Paul Haven contributed to this report.