The cheque was originally worthy $10.50. Armstrong reportedly signed it before riding an elevator to the top of the 30-story-tall Saturn V rocket which propelled him to the moon.
"Here's a check for the loan,'' Armstrong said to Harold Collins, NASA's chief of mission support, to whom it was addressed.
"But don't cash it, because I will be coming back.''
Collins stayed true to Armstrong's advice and never cashed the cheque. Bidding for it started yesterday at $500.
"The check is extremely valuable because it was written on the day of the famous launch and signed by Armstrong, who was probably the Christopher Columbus of the 20th century,'' said Bobby Livingston, director of sales and marketing at RR Auction.
After placing the winning bid, Mr Staub acknowledged that he had been willing to pay up to $40,000 for the keepsake.
"I want to keep this cheque,'' he said. "I am definitely going to hold onto it and pass it on to my kids.''
Armstrong autographs are rare, as he is a notoriously reluctant signer. The value of his autograph has jumped from £475 to £5,500 in 10 years - a staggering gain of 1058%. Click here for the world's rarest living signature.
With such high appreciation levels, holding the cheque should certainly work to Mr Staub's advantage.
