It was written by second class passenger Esther Hart on Sunday April 14, 1912, and was meant to be delivered to her mother in Essex, UK.
A total of 1,500 passengers and crew died when the New York-bound liner sank, including Mrs Hart's husband Benjamin.
The letter, written on Titanic stationery, is expected to fetch between €100,000 and €120,000 when it goes under the hammer along with other Titanic collectibles.
It comes with an envelope embossed with the White Star Line flag.
Mrs Hart, who was travelling with her daughter and well-known survivor Eva Hart, writes about being ill on board.
"My Dear ones all. As you see it is Sunday afternoon and we are resting in the library after luncheon," she writes.
A total of 1,500 passengers and crew died when the Titanic sank
“I was very bad all day yesterday could not eat or drink and sick all the while, but today I have got over it."
Mrs Hart describes how she had been to a church service with Eva and goes on to talk about the trip so far.
"Tho they say this Ship does not roll on account of its size. Any how it rolls enough for me, I shall never forget it. It is very nice weather but awfully windy and cold.
"They say we may get into New York Tuesday night but we are really due early Wednesday morning, shall write as soon as we get there", she writes.
Mrs Hart and Eva were rescued by HMS Carpathia.
A biography by Eva Hart, which is also due to be sold alongside the letter, details the moment her mother later found the letter in the pocket of her husband's coat.
Andrew Aldridge, from Henry Aldridge and Son Auctioneers, said: "The importance of this legendary item cannot be overstated, being the only known surviving example of its type to have been written on that fateful day, surviving the sinking, and having belonged to such a well-known survivor."