Abrams was also ordered to register as a sex offender, to undergo lifetime supervision after prison, and to pay a $5,000 fine.
Abrams is a former president of the Board of Neighborhood Commissioners. He resigned in August 2011 after the FBI raided his Tarzana home and confiscated computers and files.
Abrams said at the time a tumor that was removed from his spine was the root cause of a medical condition that caused bizarre behaviors out of character. He pleaded guilty in a plea agreement in September.
After the sentence was imposed Monday, Abrams, who had been free on bond under electronic monitoring, was immediately taken into custody.
Abrams' defense lawyer said he had "struggled with this problem for years. He didn't even recognize the depth of his problem."
U.S. Attorney Lana Morton-Owens told the court that Abrams "disseminated thousands of pictures." He was so prolific, she said, three separate FBI offices independently caught him distributing and receiving illegal images.
Morton-Owens said the day Abrams was arrested, he was in the process of downloading a 155-page "how-to" guide describing "what to do with a child."
Abrams was charged in February in an eight-count indictment that accused him of distributing, receiving and possessing child pornography.
Abrams resigned in August 2011 as president of the seven-member Board of Neighborhood Commissioners, which oversees the neighborhood councils that provide a link between local communities and Los Angeles City Hall.
Abrams, who had served on the board since 2008, owned a public relations firm and worked on ballot measures in Agoura Hills, Westlake Village and Walnut Creek.
According to an affidavit filed in support of a search warrant, federal authorities looking into a peer-to-peer file-sharing network were able to download more than 150 videos and images depicting child porn from a computer at Abrams' house.
While at his Board of Neighborhood Commissioners post, Abrams led a group that acts as a liaison between the many city neighborhoods and City Hall. Abrams has served on the board since 2008. The position is unpaid.
City News Service contributed to this report.