The suspect turned himself in and admitted to the crime, Duesseldorf police and prosecutors said in a joint statement.
"The involvement of this person is currently under intensive investigation," they said.
The details provide a somewhat fuller picture of an account late on Saturday by a state official who announced on German television the arrest of the man that authorities had been searching for in the 24 hours since the attack.
The attack, for which the Islamic State group claimed responsibility, occurred on Friday evening at a festival to celebrate the city's 650-year history.
The suspect is affiliated with a home for refugees in Solingen that had been searched on Saturday, authorities said.
Der Spiegel, citing unidentified security sources, said that the suspect's clothes had been smeared with blood.
The police declined immediate comment on the Spiegel report.
Islamic State described the man who carried out the attack as a "soldier of the Islamic State" in a statement on its Telegram account on Saturday: "He carried out the attack in revenge for Muslims in Palestine and everywhere."
It did not immediately provide any evidence for its assertion and it was not clear how close any relationship between the attacker and Islamic State was.
Hendrik Wuest, premier of the state of North Rhine-Westphalia, on Saturday described the attack as an act of terror.
