Alexander Bateman, 48, from Harrow, was loaned the artefact, worth Â£10,000, by the family of Sgt John Fraser in 1996, allegedly for the purposes of research.
Bateman repeatedly failed to return it when asked and lied to the family compounding their loss, a court heard.
The World War Two log remains missing, Wood Green Crown Court heard.
He was found guilty of theft last month.
Judge John Dodd QC said it was "a despicable offence" abusing the trust of a war hero's widow and involving an "important historical artefact".
Sentencing Bateman, he said: "You decided to keep the log book, treating it as your own, misleading the family when they sought its return, which added to their sense of loss and betrayal."
Speaking outside court Sgt Fraser's daughter Shere Lowe, 60, said it had a been a hard and "long 14 years".
"The deception and the cruel charade, the lies, it's had it weight on our family," she said.
"My father was a great and brave man. To the world he may have been a hero, to us he was so much more. He was devoted husband and he was Dad.
"The stolen log book to anyone else is just a commodity. To us, it was a reminder of a loved and cherished man," she continued.
Her mother Doris Fraser, 92, posted the log book to Bateman in 1996 to help with his research into the airmen's Dambuster mission.
Several years later, Bateman contacted Ms Lowe in search of further information. When she asked for its return in 2003 the family received a tampered envelope carefully sliced open at the bottom, and Bateman claimed it has been lost in transit.
Doris Fraser was "physically sick" when she realised the log book was missing, the court heard.
Bateman changed his story and said he had been given the log book as a present, providing a Christmas card he claimed to be from Sgt Fraser's widow that apparently backed up his account.
In 2003 Bateman was cautioned for other historical thefts for stealing two documents and a badge from the National Archives, prosecutor Jollyon Robertson said.
On the final day of his trial, Bateman produced what he claimed was a copy of the log book, despite previously denying he had ever made such a copy.
The family said they were hopeful the original may yet exist.
A military historian who stole a Dambusters' log book from an RAF widow has been jailed for two years for his "cruel" theft.