And, earlier today, I came across this /r/LadyBoners post of the two of them, which pictures were taken from GQ's 2011 Men of the Year issue. Obviously, I had to go back and read the article again, and found this little info:
GQ: Let's talk about how you guys came up with "History of Rap," the most viral video in network late night history.
Jimmy Fallon: We were in your dressing room backstage on SNL.
Justin Timberlake: We were just shooting the shit, right?
Jimmy Fallon: You were coming on my show later that week, and I asked, "What do you want to do?" We both thought, well we could sing something. I wanted to do Toto's "Africa."We could sing that song really well together.
Justin Timberlake: We should still do it! We should do Toto's "Africa" but we should do it as characters.
Jimmy Fallon: I was thinking we'd do "Africa" as me and you at the age of thirteen. We'd be best friends and have a tape of us having a sleepover and singing "Africa." We can wear wigs and braces.
Justin Timberlake: We were sitting there, and I said, "Do you remember that guy who did the history of dance?" He did every song that had a dance or was named after a dance. It was a viral sensation. Then we just started kicking around medley ideas. Jimmy was like, "What if we did the whole history of all hip-hop and fit in as many songs as we can?"