By an act of his Privy Council on the 17th of December, 1599, James VI of Scotland decided that New Year's Day would henceforth fall on the 1st of January.
Most folks, if asked, will say that New Year's Day falls on the 1st of January each year. It was not always so, either in the United Kingdom in general or in Scotland, in particular. Come to think of it, it still isn't so in many parts of the world. New Year's Day is generally accepted as being the day that marks the beginning of a new calendar year and also the day on which the year count is incremented, but neither was that always so and still isn't so in the Jewish calendar. The 1st of January is certainly the first day of the year on the modern Gregorian calendar and it was also the first day of the year on the ancient Julian calendar as used in Rome. Despite that apparent synchronisation, January the 1st on the Julian calendar currently corresponds to January the 14th on the Gregorian calendar.
In terms of other cultures, the Hijri or Islamic New Year begins on the first day of Muharram, the first month in the Islamic calendar. In 2011, it fell on the Gregorian 26th of November. However, the Islamic year is 11 to 12 days shorter than the Gregorian year, so there's also a perennially shifting differential between the two calendars. The Hindu New Year falls according to the time and date the Sun enters Aries on the Hindu calendar, which normally means the 13th of 14th of April, depending on the Leap year. The Jewish New Year is celebrated on Rosh Hashanah, which takes place between sunset on the evening before the first day of Tishrei and nightfall on the second day of Tishrei. Strange to say, Tishrei is the seventh, rather than the first, month of the Hebrew calendar. In terms of the Gregorian calendar, Rosh Hashanah will fall between September the 5th and October the 5th. The Chinese, on the other hand, celebrate New Year's Day as the first day of the lunar calendar, corrected every three years, for solar deviations. The date normally falls between the 20th of January and the 20th of February.
Until 1599 in Scotland, the New Year began on the 25th of March, which was in line with England. However, on the 17th of December, 1599, King James VI, via an act of his Privy Council, decided that Scotland should come into line with other “well governit commonwealths.” As a result of Jamie Saxt looking over his shoulder at the likes of 'well governed' France, the date for New Year's Day was changed from the 25th of March and imposed as the 1st of January. So the day after the 31st of December, 1599, became the 1st of January, 1600. Insular England didn't make the 1st of January the official start of the year until 1752, the year it adopted the Gregorian calendar and way after James VI became James I of England, and six years after yon Bonnie Twat, Charlie Stuart, failed to make his Pa, James VIII & III.
According to the 'Register of the Privy Council', “The Kingis majestie and Lordis of his Secreit Counsall undirstanding that in all utheris weill governit commouns welthis and cuntreyis the first day of the yeir begynis yeirlie upoun the first day of Januare, commounlie callit new yeiris day, and that this realme onlie is different fra all utheris in the compt and reckning of the yeiris ...his Majestie with the advise of the Lordis of his Secreit Counsall statutis and ordanis that in all tyme cuming the first day of the yeir sal begin yeirlie upoun the first day of Januare...”
Jamie's Privy Council was a powerful legislative and administrative body, which was very useful to him. The King had much more influence over the Privy Council than he ever did over the more independently minded Scottish Parliament. The Privy Council act of the 17th December, 1599, went on to command royal officials, clerks, judges, notaries, &c., “in all tyme heireftir” to date all “thair decreittis infeftmentis charteris seasings letteris and writtis quhatsumeuir according to this p[rese]nt ordinance.” They had a shortage of commas in those days.
The reason for January the 1st on the old style Julian calendar currently corresponding to January the 14th on the new style Gregorian calendar is that the latter is marginally shorter. The number of days in the year is the essence of a calendar year and the Gregorian calendar results in a year that is about 11 minutes shorter than the 365.25 days of the Julian year. So, if you have two calendars, one calculating the length of the year according to ancient Roman practice and one, more accurately, according to the solar equinoxes, then you get a discrepancy. In fact, the Julian calendar falls further behind every year as the deviation increases by about three days every four centuries.
New Year's Day in the Julian calendar was the 25th of March i.e., the 24th of March, 1598, was followed by the 25th of March, 1599. So, New Year's Day was the day on which the year count was incremented, but it didn't mark the beginning of the calendar year; that still being the 1st of January. So, back at the tail end of 1599, or on the 1st of January, 1600, as it was, Scotland began a new year, but it was a new year according to the Julian calendar. That meant that the 31st of December, 1600, occurred 365 days later (with 1599, the previous year, having had only nine months).
It wasn't until 1752, the same year England caught up with the New Year's Day celebrations, that Scotland adopted the Gregorian. Jamie Saxt's notions about what the French might think weren't fully developed in 1582, when the majority of European countries adopted the Gregorian and the 1st of January date for New Year's Day. Earlier, in England, Henry VIII was having nothing to do with anything named after a Pope, so he stuck to Julius Caesar's calendar, introduced in 45 BC, and so did his successors, from Edward VI all the way through to George II. The Gregorian calendar was introduced by a bull of Pope Gregory XIII; dated the 24th of February, 1582.
It took Jamie's pride and joy, the United Kingdom of Great Britain and Northern Ireland, nearly two hundred years to deal with the combined change. The Gregorian was adopted in the United Kingdom under what is known as 'Chesterfield's Act' or the 'Calendar Act of 1752', which revised the way that leap years were calculated and dropped the necessary 11 days in order to synchronise with the newly adopted, solar-based Gregorian calendar year. Wednesday, the 2nd of September, 1752, was followed by Thursday, the 14th of September, 1752. Scotland lost zero days in 1600 after changing the date of New Year's Day, but it lost the same 11 days as England, Wales and Ireland in 1752, when the Gregorian was adopted. If they'd changed back in 1582, they'd have lost only 10 days.
Incidentally, the reason the UK tax year starts on the 6th of April is that, back in 1752, the authorities didn't want to lose 11 days' tax revenue in that year, so they moved the start of the tax year forward from the 25th of March and it's been that way ever since.