Except for Washington's first inaugural, when he was sworn in on April 30, 1789, all presidents until 1937 were inaugurated in March in an effort to avoid bad weather. The 20th Amendment to the Constitution (passed in 1933) changed the inaugural date to January 20. Franklin Delano Roosevelt's Second Inauguration was the first to have been held on that date.
The date of January 20th for the presidential inauguration was established by the 1933 ratification of the Twentieth Amendment, which changed the start date of the new presidential term from March 4th.
The reason given was that due to the modern conveniences of better communications, the election results could be confirmed faster than in olden times. They did not want to make our Congress and president wait until almost the end of the first quarter of the year to begin their service.