Final answer:
Reggae is the genre that combines elements of North American rock, African music, and the Rastafarian movement, originating from Jamaica in the 1960s with notable artists like Bob Marley.
Step-by-step explanation:
The genre of music that fused characteristics of North American rock and African music with elements from the Rastafarian movement is Reggae. This music style emerged from Jamaica in the 1960s and was popularized by artists such as Bob Marley and the Wailers.
Reggae's rhythmic style is known for its offbeat accents and has influences from earlier genres such as mento and calypso. Over time, it has gained international popularity and has been incorporated into the music of many other artists outside Jamaica.