He was born in Budapest, Hungary as Arnold Guttmann. He was 13 years old when he felt compelled to become a good swimmer after his father drowned in the Danube River and then took the name Hajós (sailor in Hungarian) for his athletic career because it was an Hungarian name.
In 1896, Hajós was an architecture student in Hungary when the Athens Games took place. He was allowed to compete, but permission from the university to miss class had not come easy. When he returned to the Dean of the Polytechnical University, the dean did not congratulate Hajós on his Olympic success, but instead said: "Your medals are of no interest to me, but I am eager to hear your replies in your next examination."
At the 1896 Games, the swimming events were held in the Mediterranean Sea battling the elements. The 18-year old Hajós won his two gold medals in extremely cold weather (the water temperature was about 50 degrees in Fahrenheit) with 12-foot waves crashing down on him. He won the 100 m Freestyle (1:22.2), and 1200 m Freestyle (18:22.2) and wanted to win all three distances, but the start of the 500 m was much too soon after the finish of the 100 m. Before the 1200 m race, he smeared his body with a half-inch thick layer of grease, but it proved to be of little protection. He confessed after winning the race that, "my will to live completely overcame my desire to win." While at a dinner honoring Olympic winners, the King of Greece asked Hajós where he had learned to swim so well. Hajós replied: "In the water." He was the youngest winner in Athens.
Prior to the Athens Olympics, Hajós was 100 m Freestyle European swimming champion in 1895 and 1896. A versatile athlete, he won Hungary's 100 m sprint championship in 1898, as well as the National 400 m hurdles and discus titles. He also played forward on Hungary's National soccer championship teams of 1901, 1902, 1903.
In 1924, Hajós, an architect specializing in sport facilities, entered the art competitions at the Paris Olympic Games. His plan for a stadium, devised together Dezső Lauber (who played tennis in the 1908 Summer Olympics), was awarded the silver medal, although it is noteworthy that the jury did not award a gold medal in the competition.
The best known sports facility designed by Hajós is the swimming stadion built on the Margarita Island in the Danube in Budapest, which was built in 1930, and used for the 1958 European Swimming Championships.
His brother Henrik Hajós won gold medal in 4x250 m Freestyle swimming at 1906 Olympic Games in Athens.