Understandably, Paul got excited. Filled with pride, he drove his ailing grandmother by the new company the next day, so he could show off his new place of work. The employer never called me, and never called Paul, either. For some reason he changed his mind, and didn't have the decency to let anyone know. The reason I tell this story is to warn you that even when the cat seems to be in the bag, it ain't over 'til the fat lady sings.
Offers sometimes have strings, or contingencies attached.
Provide proof of your past employment, salary, or military service. Very often, these contingencies must be satisfied before you can to report to work or receive a paycheck. If everything about the new position is satisfactory, go ahead and accept the offer. If you're expecting an offer from a second company, you should let the second company know about your offer right away, so they can speed up their decision. That way, you'll avoid jeopardizing one deal for the sake of another.