"During interrogation by the Shin Bet (security service), Hamam Masalmeh confessed to running down the soldiers as part of a planned attack," the statement said of the November 5 incident in which the soldiers were injured.
It added that the accused was an activist in Islamist militant group Hamas.
Masalmeh turned himself in the day after the nightime attack insisting it had been a road accident.
Police said the 23-year-old driver, from a village near Hebron was expected to be charged "within the next few days."
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They said he told interrogators he was influenced by a hit-and-run attack earlier on November 5 in which a Palestinian from east Jerusalem ran down a group of pedestrians in the city killing a policeman.
In that incident, the driver was shot dead by police at the scene.
Masalmeh claimed he was also angered by images from Israel's bloody summer war in Gaza, police said.
The attack on the soldiers was the third of its kind in a fortnight.
On October 22, another Palestinian rammed his car into passengers at a Jerusalem tram stop, killing a young woman and a baby.
He was shot dead by police as he attempted to flee on foot.