He reportedly said his actions were in self defence. Following the shootings he fled the state to his home in Illinois just 10 miles away, where he was arrested and charged with murder a day later.
Mr Rittenhouse will now be sent back to Wisconsin, but it is unclear if he will go immediately.
The shootings happened as demonstrators took to the streets to protest the 23 August shooting of Jacob Blake, a Black man, by a white police officer trying to arrest him.
Mr Blake was shot seven times in the back and is paralysed from the waist down.
Court documents say that Mr Rittenhouse shot and killed Mr Rosenbaum after he threw a plastic bag at him, missing him, and then tried to wrestle his rifle away.
Prosecutors claim that members of the crowd yelled “Get him! Get that dude!” and tried to beat him up.
Mr Rittenhouse tripped, and while on the ground, Mr Huber hit him with a skateboard and tried to grab the rifle.
He apparently opened fire, killing Mr Huber and wounding Gaige Grosskreutz, who was holding a handgun. The three victims and Mr Rittenhouse are all white.
The charges he faces include first-degree intentional murder. If convicted he could face life in prison. He is also charged with attempted intentional homicide and a misdemeanour of underage possession of a firearm.
In what has become a highly-politicised case, Mr Rittenhouse is portrayed as a domestic terrorist by some on the left, and as a patriot exercising his right to bear arms by some on the right.
With reporting from The Associated Press