They named him as Hussam Dwayat, and said officers had been gathering evidence at his address in the Sur Baher neighbourhood.
Police said Hussam Dwayat had no known ties to militant groups
The BBC's Tim Franks, who witnessed the attack, said that within a few minutes a stretch of Jerusalem's city centre had been turned into a blood-soaked mess.
From his office window, our correspondent says he saw the bulldozer ram a bus again and again until it flipped onto its side.
He says he ran out into the street where the bulldozer had left in its wake cars and taxis skewed across the road, some crushed, their occupants still inside.
Israeli police say the attacker was working for a construction firm laying the foundations for a new railway system.
'Natural' response
Israeli government spokesman Mark Regev told the BBC that an initial inquiry indicated the attacker had been acting alone.
Prime Minister Ehud Olmert called the incident a terrorist attack, and condemned it as "an act of senseless murderous violence".
An aide to the Palestinian Authority President, Mahmoud Abbas, said the attack was an attempt to wreck peace negotiations, and urged a restrained response from Israel.
The Palestinian Islamist movement Hamas, which controls Gaza and is maintaining a fragile truce with Israel, denied responsibility.
But Hamas added that it was a "natural" response to "a continued aggression against our people in the West Bank and Jerusalem".
Cabin struggle
The bulldozer, which was heading towards the city's largest open-air market, upended a bus and ran over several cars.
One eyewitness told the BBC: "I saw [the bulldozer driver] crashing cars and going into the bus... He wanted to kill as many as he could."
Another eyewitness, Yaakov Ashkenazi, an 18-year-old seminary student, told the Associated Press news agency: "I saw the bulldozer smash [a] car with its shovel. He smashed the guy sitting in the driver's seat."
MAJOR JERUSALEM ATTACKS
March 2008 Gunman kills eight at west Jerusalem religious college
2004 Three suicide attacks, one on a bus, kill a total of 20 people
2003 Four suicide bombings in buses and markets kill a total of 55 people
A security guard from a nearby bank told our correspondent that he had shot the driver, bringing the bulldozer to a halt.
But then the vehicle suddenly started down the road again.
At one point, our correspondent saw two or three men inside the vehicle's cabin, struggling with the driver and causing the cabin to shake violently.
One of the men, a police officer who arrived on the scene by motorbike, described how he dealt with the attacker.
"As he was driving I climbed the tractor stairs... I also shot him with two bullets, and made sure he was neutralised - and that was the end of the incident," Eli Mizrahi told AP.
Attacks by Palestinian militants in Jerusalem have been a rare occurrence in recent years, with none of their trademark suicide bombings since September 2004.
The last deadly attack was in March this year when a gunman killed eight students in a seminary before he was shot dead.
1. Palestinian man driving a bulldozer begins his rampage down Jaffa Road in West Jerusalem, hitting several vehicles. 2. Travelling towards the Mahane Yehuda market, he rams a passenger bus several times before it overturns. 3. The bulldozer is eventually brought to a halt after the driver is shot following a struggle in the cab. At least three people are killed and dozens injured, some of them seriously.
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