Paddock was born in Gainesville, Texas to Charles H. and Lulu (Robinson) Paddock. His family moved to Pasadena, California when he was a child. After serving in World War I as a lieutenant of field artillery in the U.S. Marines, Paddock studied at the University of Southern California. There he became a member of the track and field team, and excelled in the sprint events. He won the 100 and 200 m in the first major sporting event after the war, the 1919 Inter-Allied Games, in which soldiers of the Allied nations competed against each other. Paddock was the first person named "The fastest man alive".
In 1920, Paddock represented his country at the 1920 Summer Olympics in Antwerp. In Belgium, he had his greatest successes, winning the 100 m final, while placing second in the 200 m event. With the American 4 x 100 m relay team, Paddock won a third Olympic medal. Paddock became famous for his unusual finishing style, leaping towards the finish line at the end of the race.
The next year, he ran the 110 yd, which is slightly more than 100 m, in 10.2 seconds. It wasn't until 1956 that the World Record for the 100 m became lower than Paddock's time. Paddock broke or equaled several other World Records over Imperial distances.
At the 1924 Olympics, Paddock again qualified for both the 100 and 200 m finals, but he was less successful than four years earlier; he finished 5th in the 100 m and won another silver medal in the 200 m. Paddock was not a part of the relay team. In Chariots of Fire, the 1981 Oscar-winning film about those races, Paddock was portrayed by Dennis Christopher. In 1928, Paddock participated in his third Olympics, but did not reach the 200 m final.
During his athletic activities, Paddock also held management positions in several newspapers; his father-in-law was newspaper publisher Charles H. Prisk. In the late 1920s he also acted in a few movies. Paddock served on the personal staff of Major General William P. Upshur beginning at the end of World War I.