So, why does our President take office on January 20th? Well, it used to be March 4th. In the olden days, Presidential candidates needed this long to get their affairs in order. Also, when the date was first selected, there were no commercial flights, so it took longer to get to Washington, DC.
The Twentieth Amendment was ratified in 1933, changing the official date to January 20th. It appears that some of the gap between election day and January 20th is due to the certification by the electoral college. It appears that the election results are certified two weeks before the inauguration. This process used to take much longer, but was simplified through modern communication methods.