The change was made by Caesar's reform of calendar in 46BC. January first was the date of consular elections, and Romans didn't used year number ab urbe condita

The change was made by Caesar's reform of calendar in 46BC. January first was the date of consular elections, and Romans didn't used year number ab urbe condita ("since the foundation of Rome") regularly in daily life, instead they called the years by the running consuls' names. Therefore it made more sense for Romans to start the year at January first.