The show will commemorate Bob's contributions to music this week by featuring various artists covering many of the late singer's popular tracks.
Hill will appear on Thursday, May 12 to cover two of Bob's songs while Richards will take the stage the night before on Wednesday, May 11.
The musicians join previously announced guests Ziggy Marley, Chris Cornell, Jennifer Hudson, Jakob Dylan and Lenny Kravitz in the celebration.
Bob's son Ziggy, who welcomed a baby boy with wife Orly Agai in February 2011, will kick off the tribute on Monday night.
Fallon was recently announced as a virtual guide for the Universal Studios tour in Hollywood.