Britain's interior ministry said the far-right extremist group, National Action, was being banned under the Terrorism Act as it had been assessed to be "concerned in terrorism".
The move means that supporting or being a member of the organisation will be a criminal offence, carrying a potential 10-year prison sentence, the Home Office said in a statement.
"National Action is a racist, anti-Semitic and homophobic organisation which stirs up hatred, glorifies violence and promotes a vile ideology, and I will not stand for it," said Rudd, announcing the ban.
Lawmakers will debate the legislation on Wednesday and it will likely come into force two days later.
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The ban follows the conviction last month of far-right extremist Thomas Mair, who was jailed for life for murdering pro-Europe lawmaker Jo Cox a week before Britain's referendum on membership of the EU.
National Action, whose campaigns have included a "Miss Hitler competition", posted messages on Twitter after the opposition Labour MP's killing in June, voicing support for Mair.
The group gloated on its website about the media outrage that ensued after it tweeted "#VoteLeave, don't let this man's sacrifice go in vain," alongside a picture of the Nazi-inspired killer.
The interior ministry said the decision to outlaw National Action was taken before Mair's trial but the order was delayed so as to not influence the proceedings.
Under the legislation, a group deemed to be "concerned in terrorism" could be one that commits or prepares for acts of terrorism, or promotes or encourages terrorism, the ministry said.
National Action describes itself on its website as a "growing community of young Nationalists... United in a mission to save our race and generation".