The celebration of the new year is the oldest of all holidays. It was first observed in ancient Babylon about 4000 years ago. In the years around 2000 BC, the Babylonian New Year began with the first New Moon (actually the first visible cresent) after the Vernal Equinox (first day of spring).
The beginning of spring is a logical time to start a new year. After all, it is the season of rebirth, of planting new crops, and of blossoming. January 1, on the other hand, has no astronomical nor agricultural significance. It is purely arbitrary.
The Babylonian new year celebration lasted for eleven days. Each day had its own particular mode of celebration, but it is safe to say that modern New Year's Eve festivities pale in comparison.
The Romans continued to observe the new year in late March, but their calendar was continually tampered with by various emperors so that the calendar soon became out of synchronization with the sun.
In order to set the calendar right, the Roman senate, in 153 BC, declared January 1 to be the beginning of the new year. But tampering continued until Julius Caesar, in 46 BC, established what has come to be known as the Julian Calendar. It again established January 1 as the new year. But in order to synchronize the calendar with the sun, Caesar had to let the previous year drag on for 445 days.