A draft proscription order will be laid against Wagner Group in Parliament on Wednesday.
The group has played a prominent role in the Russian invasion of Ukraine since it was launched in February 2022.
The order will mean that, once passed, it is illegal to be a member of or support Wagner Group.
Wagner’s assets can also be categorised as terrorist property and seized.
Certain proscription offences can be punishable by up to 14 years in jail.
Proscription of the group comes after consideration of the nature and scale of the organisation’s activities as well as the threat they pose to British nationals abroad, the Home Office added.
Home Secretary Suella Braverman said: “Wagner is a violent and destructive organisation which has acted as a military tool of Vladimir Putin’s Russia overseas.
“While Putin’s regime decides what to do with the monster it created, Wagner’s continuing destabilising activities only continue to serve the Kremlin’s political goals.
“They are terrorists, plain and simple – and this proscription order makes that clear in UK law. Wagner has been involved in looting, torture and barbarous murders. Its operations in Ukraine, the Middle East and Africa are a threat to global security.
“That is why we are proscribing this terrorist organisation and continuing to aid Ukraine wherever we can in its fight against Russia.”
It comes after Wagner chief Yevgeny Prigozhin was killed in a plane crash last month.
The crash occurred exactly two months after Mr Prigozhin mounted a short-lived armed rebellion against Russia’s military leadership, posing the biggest challenge to President Vladimir Putin’s authority in his 23-year rule.