Jaco was born John Francis Pastorius III, the first of three sons born to John Francis Pastorius II and Stephanie Katherine Haapala Pastorius. He had Finnish, German, Swedish, and Irish ancestry. Although Jaco was born in Norristown, Pennsylvania, the family subsequently moved to Fort Lauderdale. Jaco went to elementary and middle school at St. Clement's Catholic School in Wilton Manors, and he was an altar boy at the adjoining church. He went to high school at Northeast High in Oakland Park. He was a talented athlete with skills in football, basketball, and baseball, and he picked up music at an early age. He took the name Anthony at his confirmation.
He loved basketball, and often watched basketball with his father, whose nickname was Jack. Jaco's nickname was influenced by his love of sports and also by the umpire Jocko Conlan. He changed the spelling from Jocko to Jaco after the pianist Alex Darqui sent him a note. Darqui, who was French, assumed the name was spelled Jaco; Jaco liked the new spelling.
Originally a drummer, following in the footsteps of his father, stand-up drummer Jack Pastorius, Jaco switched to bass at age 15, after suffering an injury to his wrist. In about 1970, he began playing in a nine-piece horn band at the time called Las Olas Brass, which covered popular material of the day by Aretha Franklin, Otis Redding, Wilson Pickett, James Brown and the Tijuana Brass.