The following information (extracts) has been copied from WIKI
"Don't Worry, Be Happy" is a song by musician Bobby McFerrin. Released in September 1988, it became the first a cappella song to reach number one on the Billboard Hot 100 chart, a position it held for two weeks.
The song's title is taken from a famous quote by Meher Baba.
The original music video stars Robin Williams and Bill Irwin
Listen to the song here
By the way its not sung by Bob Marley as the website suggests.