The copy is believed to be the last one the dictator put his name to before he committed suicide in April 1945.
He gave it to an unidentified senior member of his staff in what is said to be a last defiant gesture in the hope his Nazi ideology would continue after his death, the 'Daily Mail' reported.
Experts say that his signature at the time was rushed and resembled little more than a squiggle, a reflection of his scrambled state of mind at the time.
The copy of Mein Kampf - My Struggle - was a limited print-run from 1939 to mark Hitler's 50th birthday.
Underneath his autograph he wrote the date of March 5, 1945.
At the time Hitler had taken up permanent residence in his bunker under the Reich Chancellery in Berlin while the Russians advanced from the east and British and Americans from the west.
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On April 30 - 12 days before the end of World War II - he shot himself moments after his mistress, Eva Bruan, committed suicide by biting on a cyanide capsule.
The book was acquired many years ago by a British man from an American collector. He is now selling it on February 14 at an auction, with a pre-sale estimate of 5,000 pounds.
"The book is itself rare but this one bears Hitler's signature with the date of March 5th 1945," Richard Westwood-Brooks, of auctioneers Mullocks, said.
"By March the Allied armies in the west and the Soviet Red Army in the east were making significant gains on German soil, and indeed on that very date the allies captured Cologne. Hitler, in retreat in his bunker in Berlin could only await the inevitable total destruction of his Third Reich," he said.
"But it is also well known that he believed that via some miracle some sort of surprise counter attack by the German army would turn the tide in his favour," Westwood-Brooks said.
"So on March 5 he presented this book, signing it with his bizarre signature. We don't know to whom he gave the book, but it was probably a senior member of his staff, and it is quite possible that it was given as a parting gift," he added.
"The signature is also significant as it shows how much his mental state had degenerated and he must have known his inevitable fate," he said.