The students attended North Seattle College, which said several students are in critical condition, while other students and a North employee had serious injuries.
"Because the deceased were international students, government officials are working to contact next of kin," the school said. "We extend our deepest condolences to the families of these deceased students, as well as to the students and employee who sustained injuries."
In the hours after the accident, fire officials said 44 people were hospitalized, 12 of whom were in critical condition.
Those most seriously injured were taken to Harborview Medical Center. As of Thursday evening, two people were still in critical condition and nine were in serious condition. They were in intensive care, spokeswoman Susan Gregg said.
Four others were still at Harborview and were listed in satisfactory condition. Thirty-one patients were transferred to other hospitals, and two had been released.
Some people were treated at the site of the crash, which involved four vehicles, on State Route 99, officials said.
The duck boat tour operator issued a statement after the crash.
"Ride the Ducks of Seattle wishes to express its sincerest condolences to the family and friends of the people who were killed and those that were injured," it said.
The operator said it has voluntarily pulled all its vehicles from city streets for now, according to Mayor Ed Murray.
Ride the Ducks of Seattle said the duck boat and a bus from Bellair Charters were involved in the accident.
Seattle Police Detective Patrick Michaud told CNN that all the people who died were bus passengers.
A nurse who was walking along the bridge when the crash occurred said there was a lot of blood, and she saw one body on the road. She called the scene "traumatic" with a lot of blood.
The people on the bus were employees and students in the international program at North Seattle College, the school said. North Seattle College has more 1,000 international students from more than 50 countries.
Seattle police tweeted that Aurora Bridge between downtown Seattle and the Fremont neighborhood was closed in both directions to pedestrian and vehicle traffic.
Photos from the scene showed the wrecked vehicles being surrounded by scores of firefighters. About 90 first responders rushing to the scene, Lt. Sue Stangl with the Seattle Fire Department said.
It is unclear why the duck boat -- a street vehicle that can double as a boat -- hit the bus as they drove across the six-lane bridge, Stangl told reporters.
The speed limit on the bridge is 40 mph.
Aurora Bridge history
Aurora Bridge has seen tragedy before involving buses.
In November 1998, a commuter bus plunged off the busy bridge after its driver was shot and thrown from the vehicle, then Seattle police spokeswoman Christie-Lynne Bonner said.
The vehicle, which consisted of two bus carriers connected in the middle with accordion-like flexibility to help in turns, plunged 50 feet, hit an apartment building's roof in the Fremont neighborhood and ended up upright, albeit split in two.
At least three people died in that incident, while many more were hospitalized.
Popular amphibious buses
Duck tours -- a popular option for tourists in many cities around the United States, in which people catch the sights rolling on roads or floating on waterways -- have been in accidents before.
On July 2010, two Hungarian students on a duck boat in Philadelphia's Delaware River died and at least 20 more were injuries when a sludge barge towed by a tugboat plowed into the disabled, 33-foot "Ride the Ducks" vessel. That amphibious boat, along with its 35 passengers and two crew members, were then forced into the water.
Earlier this year, a Rides the Ducks boat in Philadelphia was involved in a deadly accident with a pedestrian.