Before being banned, Jones's Twitter page had accumulated almost 900,000 followers, while the Infowars page had accrued around 430,000.
Jones was suspended from Twitter for one week last month after he posted a video in which he said, "Now is time to act on the enemy before they do a false flag".
As part of the ban, Jones will not be able to create new accounts on Twitter or take over any existing ones.
A post on the Twitter Safety account said the company took the action as a response to content posted yesterday after the much publicized senate hearing involving Facebook and Twitter. Before the hearing began, Jones and his followers surrounded Oliver Darcy, a reporter at CNN who has covered InfoWars and Twitter. In a tweet, it said it would continue to monitor reports about other accounts potentially associated with Jones or Infowars, and will "take action" if it finds any attempts to circumvent the ban.
The "Infowars" host stormed around Capitol Hill for hours, streaming appearances of himself on Twitter and Facebook outside the hearings where social media executives were testifying.
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Jones is now being sued in Texas by two Sandy Hook parents, seeking at least $1 million (£0.77 million), claiming that they have been the subject of harassment driven by his programs.
In the video, Jones confronts Darcy by calling him 'the equivalent of like the Hitler Youth'.
The exchange became heated once Jones touched Rubio's shoulder, which prompted Rubio to say, 'Hey, don't touch me again, man'.
Twitter's first punishment was minor compared to the repercussions that Jones and InfoWars faced from other tech companies just days before.
Jones' bread and butter is shouting over-the-top grievances and conspiracy theories in videos that he shares on social media, radio and his own websites. Thus far, efforts to hold Jones accountable to the community guidelines of sites he leveraged have resulted in a almost 50 per cent loss of viewership to Infowars.
Jones is now active on Facebook; his suspension there recently expired.