Since 1937 the President is sworn into office on the 20th of the January after the presidential election, why is this so?
Section 1. The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
Prior to that, the inauguration date used to be March 4 for both the presidency and the congressional sessions.
This article by Boston explains why it is held on January 20.
Basically, a 4 month transition period proved too lengthy and were harmful at times when the lame-duck period is too long.
Lawmakers realized that a substantial amount of time was needed between the election and inauguration. Local officials had to gather the election returns, and the winning candidate needed time to select a Cabinet and travel to the Oval Office.
However, the introduction of modern technology rapidly sped up this process. Election returns could be counted much faster, and elected officials could travel to the capital in a few days rather than several weeks or months. Thus, the four-month lame duck period proved unnecessary – and, at times, even harmful. When Franklin D. Roosevelt was elected in 1933, the lengthy transition period prevented him from immediately addressing the economic challenges that the nation faced during the Great Depression.