Aniruddha Sherbow, 42, was given the prison term by a federal court in the United States.
According to the government's evidence, he had been harassing Gabbard since February 2011, including making threats via email and telephone.
The charges relate to two such threats, made in August 2013.
On August 1 last year, Sherbow left a voicemail message on Gabbard's phone in which he threatened to kill her. Gabbard was in Washington, DC, when she received the message.
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The subject and body of this e-mail also contained threats directed at Gabbard.
Sherbow was arrested in Tijuana by Mexican law enforcement officers and was handed over to the FBI.
US attorney for the District of Columbia, Ronald C Machen, said Sherbow entered a plea of nolo contendere on February 21, 2014, in the Columbia District Court, to two counts of transmission of threats in interstate commerce.
Under a nolo contendere plea, a defendant is convicted of the offense, accepts responsibility, and agrees that the government could prove him guilty beyond a reasonable doubt.
Following his prison term, Sherbow will be placed on three years of supervised release. During that time, he is barred from any direct or indirect contact with Gabbard.
District Judge Reggie Walton also ordered Sherbow to pay USD538,282 in restitution to the US government, as reimbursement for security expenses incurred as a result of his threats.
The judge also ordered Sherbow to get a mental health evaluation and treatment, if necessary.
Sherbow has lived in New York, California, Mexico and Hawaii.