Robert 'Joe' Halderman, formerly a producer at CBS, had demanded $2m (£1.3m) not to reveal details of affairs that the chat show host had had with members of his staff.
Letterman subsequently confessed to the infidelities live on air in October.
Halderman, who was a producer on 48 Hours Mystery, had discovered the information by reading the diary of former girlfriend, Letterman staffer, Stephanie Birkitt.
As well as the six month sentence, the blackmailer received 1,000 hours of community service.
Letterman recently said in a TV interview that that case had badly shaken him, saying, "You take a look at the explosion, and it knocks you down".
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