The first known Christmas card was sent to King James I of England and his son, Henry Frederick, Prince of Wales in 1611 by German physician Michael Maier, an advisor to Rudolf II, the Holy Roman Emperor.
This suggests that Christmas cards were already being exchanged in Europe at the time, but they didn't really catch on until 1843, when British inventor Sir Henry Cole commissioned the painter John Calcott Horsley to create a design that Cole had mass-produced.
When Queen Victoria started sending official palace Christmas cards later that decade, the tradition was born.