Halderman, an Emmy Award-winning producer, pleaded guilty last month to threatening to reveal the married talk-show host's sexual relationships with female staffers if Letterman didn't pay him $2 million.
Instead of paying Halderman, Letterman turned him into the authorities and admitted his misdeeds on "Late Show with David Letterman."
The New York Daily News said Halderman's plea agreement bans him from making public any private information he knows about Letterman.
Halderman reportedly also will be placed on probation for 4 1/2 years and has been ordered to perform 1,000 hours of community service after he is released from prison.
In addition, the producer may not have any contact with the talk-show host until 2018, the Daily News said.
"He's been to every hot spot in the world -- Iraq, Afghanistan, Somalia," his defense attorney, Gerald Shargel, told the newspaper. "I think he can handle Rikers Island."
Halderman began his jail sentence Tuesday after the sentencing.