They were believed to be returning from an exchange in Barcelona, where the plane took off from on Tuesday morning, bound for Dusseldorf.
The Joseph-Koenig Gymnasium, in Haltern am See, near Dusseldorf, confirmed during a press conference that the students and teachers were on the plane.
The French Prime Minister Manuel Valls has said there were no survivors.
The cause of the crash remains unclear and there were contradictory statements about whether the plane made a distress call.
Haltern Mayor Bodo Klimpel told reporters at a press conference: Initially I would like to say that the town is deeply affected and saddened.
"The state of shock that is palpable everywhere, that is pretty much the worst that anyone could imagine.
"On the boarding list of the plane which crashed there are 16 students from our school and there are two teachers.
"They were listed by name and the school director has received confirmation from Spain that the students did board the plane, with the teachers accompanying them.
"Rescue services have not been able to reach the crash site which means we have no final confirmation of the worst, however we have to assume the worst."
Students at the school were sent home earlier in the day and parents of the children on the plane have gathered at the airport, according to German media.
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Family members arriving at the airport have been taken from the main terminal to a nearby building.
Airport employees partly covered the building with sheets to keep the relatives out of the eye of the public.
The airline is reporting that 67 Germans were on board the plane, which descended from its cruising altitude for eight minutes before crashing.
In Dusseldorf, the destination airport, family members arriving at the airport were taken from the main terminal to a nearby building. Airport employees partly covered the building with sheets to keep the relatives out of the eye of the public.
Chancellor Angela Merkel said the crash had "plunged us into deep mourning in Germany, France and Spain".
She added: "What concerns me now is the extent of the suffering, which this catastrophe has brought to so many people.
"My thoughts and condolences, and those of the entire government, go out to the people who have lost their lives, including many compatriots."
She added her thoughts were "with those people who so suddenly lost their lives, among them many compatriots."
Merkel said she would travel to the region the plane crashed in on Wednesday, a day after her foreign and transport ministers were heading to the crash site.
She has also urged people not to speculate on the cause of the crash, which remains a mystery.
Footage of the crash scene has emerged.
The first photos from the ground have been coming in.