A military policeman hit by the vehicle as it plowed through a crowd also died, taking the toll among onlookers to six.
Mourners laid flowers at the monument in the city of apeldoorn
The motive of the 38-year-old driver, identified by local media as Karst Tates, was unclear. No weapons or explosives were found when police searched his house and there were no signs that others were involved in planning the attack.
Authorities plan an investigation into the security measures surrounding the parade, the Justice and Interior ministries said in a statement .
The public prosecutor said Tates died overnight. He had been charged with an attempted attack on the royal family and had told police he had deliberately targeted the royals.
The prosecutor said Tates came from Huissen, a small town about 40 km (25 miles) south of Apeldoorn.
Newspapers cited his neighbors as saying he was a withdrawn man who lived alone. He had lost his job at a security firm and was due to move house.
The military policeman died from his injuries, the Defense Ministry said. Eight people are still in hospital, with one woman in a critical condition following the attack on the Queen's Day national holiday.