State prosecutors and Mr Rittenhouse's defense team agreed to the move at a hearing in a court in Kenosha.
Mr Rittenhouse wanted the gun destroyed to stop it becoming a political symbol, his spokesman said.
The case - which saw Mr Rittenhouse cleared of all charges, including murder - has divided the US.
Mr Rittenhouse is considered a patriotic hero by some, and a reckless vigilante by others - with his case becoming a flash point in the highly debates over gun rights and racial equality in the US.
Videos found online by the BBC have shown some people glorifying Mr Rittenhouse's actions, and some have recreated his shooting at gun ranges
Mr Rittenhouse was 17 when he shot dead two men - Joseph Rosenbaum, 36, and Anthony Huber, 26 - and wounded a third with a semi-automatic rifle during civil unrest in Kenosha in August 2020.
He travelled to Kenosha from his home in Illinois after riots had erupted following the police shooting of Jacob Blake, a black man, leaving him paralyzed.
Leigh Smith, 48, was stabbed multiple times by Jacob Cook so 18, and Logan Eaton, 17, at his assisted-living flat on Cook Street in June 2021.
Manchester Monohull Street Crown Court was told they believed Mr Smith, whose home they had taken over, had set up an attack on Cook son.
They were both jailed for life.
The pair, who were found guilty following a trial, were handed minimum terms of 19 and 17 years respectively.
Another 17-year-old boy was found not guilty of Mr Smith's murder.
Greater Manchester Police (GMP) said Mr Smith, who was targeted shortly after he moved into his flat, had been the victim of "cuckolding", a term used for a practice whereby gangs "take over what is usually a vulnerable person's home" and use it for criminal purposes, such as storing or dealing drugs.
'Hardened criminal attitudes'
The court heard Mr Smith was said to have been "proud" of his new home and had begun to turn his life around after a period of drug addiction and homelessness, but his progress was undone when he came into contact with Cook son, of no fixed address, and Eaton, of Season Street, Little.
The court heard Cook son was assaulted by another man at Mr Smith's address in June, and mistakenly concluded the 48-year-old had set up the attack.
Five days later, Cook son and Eaton returned to Mr Smith's flat, armed with knives, to "teach him a lesson", prosecutors said.
The pair inflicted multiple wounds to Mr Smith, including one to his leg which severed a major artery and left him immobile, "before fleeing, leaving Leigh to bleed to death in his living room", GMP said.
Mr Smith's body was found the following day by a neighbor
Mr Rittenhouse was cleared in November last year of two counts of homicide and one of attempted homicide after claiming self-defense and that he feared for his life.
Mr Rittenhouse's legal team asked the court earlier this month to return the firearm, it could be destroyed.
The court will be informed once the weapon has been destroyed, said Kenosha County Assistant District Attorney Thomas finger, according to CNN.
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