Justice Secretary Chris Grayling told the Mail on Sunday newspaper: "This is a law to combat cruelty − and marks our determination to take a stand against a baying cyber-mob."
There has been increasing concern in Britain about the growing scourge of internet "trolls" who post hate-filled messages on social media, often threatening their targets.
The parents of missing girl Madeleine McCann are among the most recent victims, and last month a man was jailed for 18 weeks for what prosecutors described as "a campaign of hatred" against a female lawmaker.
"These internet trolls are cowards poisoning our national life. No-one would permit such venom in person, so there should be no place for it on social media," Grayling said.
"That is why we are determined to quadruple the current six-month sentence."
Victims have welcomed moves to take online threats seriously, and lawyers had anticipated an increase in sentences for those convicted of trolling.
"There is a public interest in having people put away for a long time. It is putting someone in fear of their life and fear of physical harm," Chris Holder, of London law firm Bristows, told AFP earlier this month.
"I think the law will develop and the sentences will go up and up."
However, freedom of speech campaigners have previously warned that criminal sanctions should be the last resort.
"Do we want to criminalise every social conduct that we find problematic?" Barbora Bukovska, a senior director at campaign group ARTICLE 19, said earlier this month.
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