Electrons from everywhere. To make it easier to understand, a battery has got chemical reactions running that sends electrons out through the negative terminal of the battery.
As you will know, an electron can only move that freely if it is placed in an electric field (generated by some potential difference - presence of charges). So, in this case it goes to the positive terminal where the reaction is in need of these electrons. There is more to it, but this is the main point.
These electrons are not that free to make it individually to the other terminal in that fraction of time. These electrons have random velocities before the electric field came into play, but in random directions in the wire. That is, say that the number of electrons that went right is the exact same as those that came from the right.
It is due to the application of the electric field that the electrons (in the wire) move around. But they don't move at those lightning speeds, but instead collide with each other, the atoms, and move about. However, the energy has been transmitted all that distance quickly.