The letter by 33-year-old Wallace Hartley describes the grandeur of the luxury liner, calling Titanic "a fine ship." He also praise his fellow musicians as "a fine band".
Hartley, from Colne in Lancashire, is remembered for playing on with his band in an effort to keep the stricken vessel's passengers calm.
The letter to his parents sent on the day the Titanic set sail on its maiden voyage from Southampton on April 10 1912, was auctioned at Henry Aldridge and Son in Wiltshire.
The letter is written on official White Star Line notepaper and bears the printed heading "On board RMS Titanic".
Also Read
In the letter, Hartley wrote that he "missed coming home very much & it would have been nice to have seen you all if only for an hour or two".
Auctioneer Andrew Aldridge said he was "unaware of any other surviving letter written by Hartley on board the ship".
"This letter mentions the band and alludes to the wealth on board the ship - implying that some of it would make its way to the band in the form of gratuities," Aldridge said.
RMS Titanic - a British passenger liner - sank in the North Atlantic Ocean on April 15, 1912 after colliding with an iceberg during her maiden voyage from Southampton, UK to New York, US.
More than 1,500 lives were lost in the accident.