His mother, Yome, is Thai and his father, Jimmy, is American; they met while his father was serving as a staff sergeant in the United States Army. Johnny was born on an Army base, and spent much of his early childhood as an "Army brat," moving to several bases before his father left the Army and settled the family in the Orlando area.

Damon was selected by the Kansas City Royals in the first round of the 1992 amateur draft out of Orlando's Dr. Phillips High School; he was the 35th pick overall. He played for the Royals from 1995 to 2000, and spent 2001 with the Oakland Athletics. He spent 2002 to 2005 with the Boston Red Sox before signing as a free agent with the New York Yankees on December 20, 2005.

As a part of his exercise routine, Johnny admits to pursuing cars from one end of his block to the other on foot. "I live on a street (in the Orlando area) where the speed limit is 25 miles an hour and the police enforce it. At night I'd wait out there and when a car came by I would race the car home, so I think I can go at least 25 miles an hour. I scared some of the people, seeing a caveman racing after cars," said Damon in a Providence newspaper article early in 2004.