Owners of weapons such as knives, knuckle-dusters and rifles are being offered cash to hand them in to police.
The Offensive Weapons Act comes into force next year, and items banned under it can be surrendered under a three-month scheme in England and Wales.
Compensation for lawful owners ranges from £2 to £5,105 for each item – but the total value of a claim must be at least £30.
The National Police Chiefs Council said the scheme would make streets “safer”.
It was already illegal to possess a knife or offensive weapon in public, but the new law makes it unlawful to possess certain rapid-firing rifles, specific types of knives and other offensive weapons in private.
While the overall scheme applies to England and Wales, compensation will also be offered in Scotland and Northern Ireland but only firearms will be covered by those schemes.
The compensation available includes:
Crime and policing minister Kit Malthouse said the weapons in question “have a high potential for causing harm”.
“Every item surrendered is one which can no longer fall into the hands of criminals,” he added.
The Offensive Weapons Act was introduced by the government in response to a spike in serious violence, including knife crime.
As well as prohibiting the possession of dangerous weapons in private, it also made it a criminal offence to sell bladed products online without verifying the buyer was aged over 18.
Graham McNulty, deputy assistant commissioner of the Metropolitan Police – who also acts as lead officer on knife crime for the NPCC – said: “The surrender scheme will enable us to remove dangerous weapons off the streets and assist in keeping our communities safe.
“Every weapon removed is possibly a life saved and I urge people to please help us make our streets safer.”