The Jolof Empire ruled what is now Senegal from the mid-14th to the late 19th century. The dish almost certainly takes its name from this empire.
Tomatoes only arrived in West Africa in the 17th century, brought by Portuguese traders along the Senegambian coast. Scotch bonnet peppers came at the same time. Both ingredients are central to modern jollof, which means the dish as we know it cannot be older than ~400 years.
The original dish, thieboudienne, used what was at hand — local fish, broken rice (often a colonial-era discard), and the seasonings of the Sahel. Jollof in its tomato-pepper-rice form spread southward, picked up local variations, and became regional in Nigeria, Ghana, Sierra Leone, Liberia, Cameroon, and beyond.