Answer by taking a quote from the following article:

Jerome John Garcia (August 1, 1942 - August 9, 1995) was an American singer-songwriter and guitarist, best known for his work as the lead guitarist and as a vocalist with the band Grateful Dead, which came to prominence during the counterculture era in the 1960s. Although he disavowed the role, Garcia was viewed by many as the leader or "spokesman" of the group. One of its founders, Garcia performed with the Grateful Dead for their entire thirty-year career (1965-1995). Garcia also founded and participated in a variety of side projects, including the Saunders-Garcia Band (with longtime friend Merl Saunders), the Jerry Garcia Band, Old and in the Way, the Garcia/Grisman acoustic duo, Legion of Mary, and the New Riders of the Purple Sage (which Garcia co-founded with John Dawson and David Nelson).

Jerry Garcia's ancestors on his father's side were from Galicia in northwest Spain. His mother's ancestors were Irish and Swedish. He was born in the Excelsior District of San Francisco, California, on August 1, 1942, to Jose Ramon "Joe" Garcia and Ruth Marie "Bobbie" (nee Clifford) Garcia, who was herself born in San Francisco. His parents named him after composer Jerome Kern. Jerome John was their second child, preceded by Clifford Ramon "Tiff", who was born in 1937. Shortly before Clifford's birth, their father and a partner leased a building in downtown San Francisco and turned it into a bar, partly in response to Jose being blackballed from a musicians' union for moonlighting.  Garcia was influenced by music at an early age, taking piano lessons for much of his childhood. His father was a retired professional musician and his mother enjoyed playing the piano. His father's extended family--who had emigrated from Spain in 1919--would often sing during reunions.  Garcia experienced several tragedies during his youth. At age four, while the family was vacationing in the Santa Cruz Mountains, two-thirds of Garcia's right middle finger was accidentally cut off. Garcia and his brother Tiff were chopping wood. Jerry steadied a piece of wood with his finger, but Tiff miscalculated and the axe severed most of Jerry's middle finger. After his mother wrapped his hand in a towel, Garcia's father drove him over 30 miles to the nearest hospital. A few weeks later, Garcia -- who had not looked at his finger since the accident -- was surprised to discover most of it missing when the bandage he was wearing came off during a bath. Garcia later confided that he often used it to his advantage in his youth, showing it off to other children in his neighborhood.  Less than a year after he lost most of his finger, his father died. Vacationing with his family near Arcata in Northern California in 1947, Garcia's father went fly fishing in the Trinity River, part of the Six Rivers National Forest. Not long after entering the river, Garcia's father slipped on a rock, lost his balance and was swept away by the river's rapids. He drowned before other fishermen could reach him. Although Garcia claimed he saw his father fall into the river, Dennis McNally, author of the book A Long Strange Trip: The Inside Story of the Grateful Dead, argues Garcia formed the memory after hearing others repeat the story. Blair Jackson, who wrote Garcia: An American Life, lends weight to McNally's claim. Jackson's evidence was that a local newspaper article describing Jose's death failed to mention Garcia was present when he died.

Where else are his ancestors from
His mother's ancestors were Irish and Swedish.