The Swedish honour is typically shared between a pop performer and a classical artist.
The pair will be invited to accept the award - worth 1 million kronor (Â£88,800) - in Stockholm in August.
The Polar Prize - founded in 1989 to honour exceptional achievements that transcend music genres - is awarded annually.
It is described in Sweden as the "Nobel prize of music" and was established by the late Stikkan Anderson, whose record company released the songs of Swedish supergroup Abba.
Bjork and Morricone will both be presented with their awards by King Carl XVI Gustaf at a gala ceremony at the Stockholm Concert Hall on 31 August.
Bjork, 44, hit the big time with her solo album Debut in 1993 but had previously had success as the lead singer of The Sugarcubes.
She also starred in Lars von Trier's Dancer in the Dark in 1999, which went on to win the Palme d'Or at Cannes, with Bjork winning the best actress award.
"BjÃ¶rk is an untameable force of nature, an artist who marches to nobody's tune but her own," said the prize committee.
Morricone, 82, has composed more than 400 film scores, including The Good The Bad and The Ugly, The Untouchables, Cinema Paradiso and The Mission.
The committee said Morricone's "congenial compositions and arrangements lift our existence to another plain".
Previous winners of the Polar Prize include Pink Floyd, Sir Paul McCartney, Quincy Jones, Dizzy Gillespie, Pierre Boulez and Ravi Shankar.
Icelandic singer Bjork and Italian film composer Ennio Morricone have won the 2010 Polar Music prize.