"The fairy tale was a present. A present of thanks to a woman whose home had been very important to him," Askgaard said.
The Bunkeflod family then sent the manuscript to another family close to Andersen, the Plum family, in whose archives the story was found. A dedication written on the document later in blue ink reads: "To P Plum from his friend Bunkeflod."
Experts believe that the neatly written document is likely the copy of an original manuscript that has since been lost.
The story is about a neglected and dirty tallow candle which finds happiness when a tinder box sees its inner beauty and lights its wick.
"The Tallow Candle had found its right place in life – and shown that it was a real candle, and went on to shine for many a year, pleasing itself and the other creations around it," Andersen wrote.
Although the tale is not at the level of Andersen's later works, it is the most important find since the 1920s, when the writer's memoirs were discovered at the Royal Library.
"This is a sensational discovery. Partly because it must be seen as Andersen's first fairy tale, and partly because it shows that he was interested in the fairy tale as a young man, before his authorship began,"Askgaard said.