After seeing the hagiographic Biggie Smalls / Notorious BIG biopic Notorious in February 2009, Simon Mayo phoned his daughter and enquired of her, "wassup wassup?" She replied, "you stupid middle-aged man." Simon related this anecdote on that week's show, later adding, "if the question is wassup wassup, what is the answer?"
By May 2014, the greeting was being used by Simon's children back towards him, with the addition of an another "wassap" and a "my father". This then got re-shortened to "wassup, wassup, wassup", rapidly became the de rigueur opening to the podcast from its first use despite the Good Doctor's initial reservations.
It has even been put to music. You can listen/download Mayo and the Muppets here. (Courtesy of The Brothers Streep.)
See seasonal variation "Wassail, wassail, wassail".