The note was written by Belfast born Dr John Simpson, the assistant surgeon on board the ship, to his mother.
It was due to be sold at an auction in New York with a $34,000 reserve price, but after hearing a campaign by relatives of the Simpson family, a donor who did not want to be named stepped in.
"It has been bought on behalf of Belfast," Dr Martin, the great-nephew of Dr Simpson, said.
"I'm absolutely delighted. I've never actually seen the original letter itself as it was last in Belfast in the 1940s."
The letter, which is dated 11 April 1912 and was written on notepaper headed RMS Titanic, was brought ashore to be posted from Cobh - the port, then known as Queenstown, where the ill-fated ship raised anchor for the final time.
"Dear mother," Dr Simpson wrote.
"I travelled from Liverpool on Monday by the 12 o'clock train and arrived on Ward at 10pm feeling pretty tired.
"I am very well and am gradually getting settled in my new cabin which is larger than my last. This seems all the time as if it was the Olympic and I like it very much.
"I am a member of the club now which is an advantage. Be sure to let me know how father gets on with his club.
"I was glad to get away from Liverpool as usual and don't intend to go up for a month or two. I found my two trunks unlocked and 5 or 6 dollars stolen out of my pocket-book. I hope none of my stamps have been stolen.
"Did I have my old portmanteau when I borrowed the kit bag? I think not."
He signed off: "With fondest love, John."
The 37-year-old went down with the ship.