The Flag of Sweden harkens back to the 16th century, and is believed to be modelled from the State Arms of Sweden, Coats_of_Arms_of_Sweden, which contains a yellow cross on blue background (constructed in the 15th century by King Karl Knutsson Bonde, Charles_VIII_of_Sweden) and on the Danish flag, the Dannebrog. The colours of the flag are the same as the ones on the seal of the three crowns, the lesser state arms. Duke Johan of Finland, son of Sweden's King Gustav Vasa, took the form of the current Swedish flag into use in 1569. Prior to this, a similar flag appeared in the coat-of-arms of the duchy under Duke Johan's rule, which is today Southwest Finland. Indeed, this yellow cross on a royal blue field found in the Southwest Finland coa-of-arms eventully became Sweden's official flag.
See also: Flag days in Sweden, Holidays in Sweden, National anthem of Sweden