The second letter is hand-written and was sent to Mr Makin in 1957 congratulating him on his engagement.
Both letters are now on permanent display at the exhibition.
Mr Makin said: "I was sorting out my paperwork and didn't want to just throw them out.
"I thought they might be of some entertainment and interest so donated them to the exhibition.
"One letter was congratulating me on my engagement and was very sweet. I was very close to Brian - he was a neighbour.
"I was the man who invented the term Beatlemania."
Louise Collier, operations manager of The Beatles Story, described the items as a valuable for the collection. She said: "I was delighted he has offered The Beatles Story the opportunity to display these valuable items for the enjoyment of the fans."