Eleven people were hurt, one critically.
The attacker was identified as Ohio State student Abdul Razak Ali Artan. He was born in Somalia and was a legal permanent resident of the U.S., according to a U.S. official who wasn't authorized to discuss the case and spoke on condition of anonymity.
Read more: Everything we know about Abdul Artan.
The FBI joined the investigation.
The Ohio State student newspaper, The Lantern, profiled Artan in August.
In the short piece, he spoke of being a transfer student to the large university and hesitation at openly praying because of his Muslim faith.
In the profile he said:
"I just transferred from Columbus State. We had prayer rooms, like actual rooms where we could go pray because we Muslims have to pray five times a day.
"There's Fajr, which is early in the morning, at dawn. Then Zuhr during the daytime, then Asr in the evening, like right about now. And then Maghrib, which is like right at sunset and then Isha at night. I wanted to pray Asr. I mean, I'm new here. This is my first day. This place is huge, and I don't even know where to pray.
"I wanted to pray in the open, but I was scared with everything going on in the media. I'm a Muslim, it's not what the media portrays me to be. If people look at me, a Muslim praying, I don't know what they're going to think, what's going to happen. But, I don't blame them. It's the media that put that picture in their heads so they're just going to have it and it, it's going to make them feel uncomfortable. I was kind of scared right now. But I just did it. I relied on God. I went over to the corner and just prayed."
The details emerged after a morning of confusion and conflicting reports that began with the university issuing a series of tweets warning that there was an "active shooter" on campus near the engineering building and that students should "run, hide, fight." The warning was apparently prompted by what turned out to be police gunfire.
Numerous police vehicles and ambulances converged on the 60,000-student campus, and authorities blocked off roads. Students barricaded themselves inside offices and classrooms, piling chairs and desks in front of doors.
Ohio State Police Chief Craig Stone said that the assailant deliberately drove over a curb outside a classroom building and then got out and began attacking people with the knife. A campus officer who happened to be nearby because of a gas leak arrived on the scene and shot the driver in less than a minute, Stone said.
Angshuman Kapil, a graduate student, was outside the building when the car barreled onto the sidewalk.
"It just hit everybody who was in front," he said. "After that everybody was shouting, 'Run! Run! Run!'"
Student Martin Schneider said he heard the car's engine revving.
"I thought it was an accident initially until I saw the guy come out with a knife," Schneider said, adding that the man didn't say anything when he got out.
Most of the injured were hurt by the car, and at least two were stabbed, officials said. One had a fractured skull.
Asked at a news conference whether authorities were considering the possibility it was a terrorist act, Columbus Police Chief Kim Jacobs said: "I think we have to consider that it is."
Surveillance photos showed Artan in the car by himself just before the attack, but investigators were looking into whether anyone else was involved, the campus police chief said.
In recent months, federal law enforcement officials have raised concerns about online extremist propaganda that encourages knife and car attacks, which are easier to pull off than bombings.
The Islamic State group has urged sympathizers online to carry out attacks in their home countries with whatever weapons are available to them.
In September, a 20-year-old Somali-American stabbed 10 people at a St. Cloud, Minnesota, shopping mall before being shot to death by an off-duty officer. Authorities said he asked some of his victims if they were Muslim. In the past few years, London and other cities abroad have also seen knife attacks blamed on extremists.
The shelter-in-place warning at Ohio State was lifted and the campus declared secure after about an hour and a half, after police concluded there was no second attacker, as rumored.
The attack came as students were returning to classes following the Thanksgiving holiday break and Ohio State's football victory over rival Michigan that brought more than 100,000 fans to campus on Saturday.
Rachel LeMaster, who works in the engineering college, said a fire alarm sounded on campus.
"There were several moments of chaos," she said. "We barricaded ourselves like we're supposed to since it was right outside our door and just hunkered down."
LeMaster said she and others were eventually led outside the building and she saw a body on the ground.
Classes were canceled for the rest of the day.
The officer who gunned the attacker down was identified as 28-year-old Alan Horujko, who joined the force in January 2015.
The initial tweet from the university's emergency management department went out around 10 a.m. and said: "Buckeye Alert: Active Shooter on campus. Run Hide Fight. Watts Hall. 19th and College."
Ohio State President Michael Drake said the active-shooter warning was issued after shots were heard on campus.
"Run, hide, fight" is standard protocol for active shooter situations. It means: Run, evacuate if possible; hide, get silently out of view; or fight, as a last resort, take action to disrupt or incapacitate the shooter if your life is in imminent danger.
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