Among the ancient peoples, New Year's Day was traditionally celebrated in conjunction with the vernal or autumnal equinox or the summer or winter solstice. In the Middle Ages it was set at the vernal equinox in the northern hemisphere, usually on March 25.
The Gregorian calendar, which is widely in use throughout the western world today, was initially decreed by Pope Gregory XIII in 1582. January 1 was declared as the first day of the new year on 1 January 1622.
This was carried forward from the previous Julian calendar. When Julius Caesar created this calendar in 45 BC, he decided that the first day of the year would be January 1st.
However, this was in keeping with the decision by the Roman senate in 153 BC. January was ruled by Janus, the Greek god, who looked both backwards, at the year past, and forwards at the new year. They decided that the first of two annual consuls would take their office on this day.
But the month January had existed since around 713 BC, when Romulus is said to have added it to the Roman lunar calendar (there were previously no months between December and March!).
So the conundrum exists: did the attributes of Janus decide the positioning of the new year or was the time of the new year decided first? We're back where we started!