They will be invited to accept the award, which includes 1 million kronor ($130,000) each in prize money, at a ceremony in Stockholm later this year.
The Polar Music Prize is Sweden's biggest music award and is typically shared by a pop artist and a classical musician. It was founded by Stig Anderson, manager of Swedish pop group ABBA , in 1989.
Prize committee Chairman Alfons Karabuda said 44-year-old Bjork personifies the border-breaking attributes sought by the committee, "bravely and without compromises."
Bjork sang in various Icelandic bands in the 1980s and rose to international fame with her solo album "Debut" in 1993. She has since released five more solo albums as well as film soundtracks and compilations. She also won the Cannes Film Festival's 2000 award for best actress for her role in Lars von Trier's "Dancer in the Dark."
"With her deeply personal music and lyrics, her precise arrangements and her unique voice, Bjork has already made an indelible mark on pop music and modern culture at large, despite her relative youth," the prize committee said in its citation.
Morricone, 71, has composed more than 400 film scores, including the iconic theme from "The Good, the Bad and the Ugly" and other spaghetti westerns directed by Sergio Leone.
The prize committee said his "congenial compositions and arrangements" help lift "existence to another plain, making the mundane feel like dramatic scenes in full Cinemascope."
"He built up a brand new kind of music that set the tone for half a century of film music, but also influenced and inspired a number of musicians in the spheres of pop, rock and classical music," the committee said in its quotation.
Last year's award was shared by British musician Peter Gabriel  and Venezuelan composer Jose Antonio Abreu.
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