The winners will receive 1 million kronor ($122,000) each and formally accept the prize from Sweden's King Carl XVI Gustaf at a ceremony in Stockholm on August 31.
Gabriel, 59, was honoured "for his ground-breaking, outward-looking and boundary-busting artistry," the organization said in a statement.
"As a composer, artist and person, Peter Gabriel has not only had a significant influence on the development of popular music -- he has redefined the very concept," the jury said.
Gabriel was a founding member of the progressive rock band Genesis in the 1960s, a group he left in the 1970s to pursue a successful solo career. He is also known for his human rights activism.
The jury meanwhile lauded Abreu, an economist and composer, for creating the music network El Sistema.
Established in 1979, the network, also known as Fesnojiv, now comprises some 30 professional orchestras and more than 300,000 youths attend its music schools and programmes.
"Driven by a vision that the world of classical music can help improve the lives of Venezuela's children, he created the music network El Sistema, which has given hundreds of thousands the tools to leave poverty."
The prize, which has been awarded since 1992 when it went to ex-Beatle Paul McCartney, has also gone to American jazz musician Dizzy Gillespie, Russian cellist Mstislav Rostropovich, British pop musician Elton John, French classical conductor and composer Pierre Boulez.