In 46 BCE Julius Caesar reformed the Roman republican calendar. Borrowing the Egyptian solar calendar and making it the official calendar of the empire, he declared January 1st to be the first day of the new year. The ancient Roman year had 10 months beginning with March, as the names of the months themselves will tell you: September means "seventh month". The Hebrew civic new year, Rosh HaShana, is on the first of the seventh month, Tishrei.
Christians had mostly observed the feast of the annunciation on March 25th as the beginning of their year until 15xx when pontifex Gregory's reform moved the new year to Jan 1st.
The date Jan 1st always occurs 8-10 days after the winter solstice. The previous two festivals, Saturnalia, and Calenda, each continue for 7 days, and are defined not with respect to the the astronomical event of solstice, but with respect to political event of the "Calends", that is a public declaration of the first day of January, and the appointment of a new consul. New years day is conventionally defined, a fictional product of inexact roman astrological calculation, rather than the observance of a celestial event. The Chinese new year and Jewish new years, on the contrary, are defined with respect to celestial events: the new moon of Adar and the new moon of Aviv-Nisan, respectively, and as such are more natural and real holidays.