Another 24 children were injured in the crash near Sierre, in the canton of Valais, close to the border with Italy.
The coach, carrying 52 people back to the Belgian towns of Lommel and Heverlee following a skiing trip, struck a wall in the tunnel head-on late on Tuesday.
Belgian PM Elio Di Rupo said it was "a tragic day for all of Belgium".
'Incomprehensible'The bus crashed shortly after 21:00 (20:00 GMT) on Tuesday.
In Brussels, the Belgian foreign ministry said most of the children were aged around 12, and the bus was one of three hired by a Christian group. The other two reached Belgium safely.
The coach is removed from the crash scene. It appears to have travelled along the right hand wall of the tunnel and collided head-on with the concrete wall (right) that provides emergency access The children had spent a week skiing in Val d'Anniviers in the Swiss Alps.
Those on board the bus that crashed were from 't Stekske primary school in Lommel, close to the Dutch border, and from Sint Lambertusschool in Heverlee, near Leuven, with Belgian media saying the numbers were roughly even.
Belgian Transport Minister Melchior Wathelet said the company that ran the coach, Toptours, had "an excellent reputation".
Continue reading the main story 13 March 2012: Bus carrying schoolchildren back from skiing holiday crashes into wall near Sierre, Switzerland, killing 22 children and six adults24 October 2001: Two lorries collide in Switzerland's Gotthard tunnel, starting a fire, with 11 people killed mainly by smoke and gas inhalation24 March 1999: A Belgian lorry catches fire in the Mont Blanc tunnel between France and Italy, leaving 39 people deadHe said: "The drivers had arrived the night before and had rested during the day before departure. It seems that the law on driving and rest periods has been respected."Both of the coach's drivers were among the dead.
Distraught relatives have been arriving at the schools in Belgium.
Swiss prosecutor Olivier Elsig told a news conference the bus was new, or nearly new, and was equipped with safety belts.
In a tunnel where the speed limit is 100km/h (62 mph), Mr Elsig said the bus collided with the right-hand wall and then hit, head-on, a concrete wall that forms part of an emergency access section. An investigation is under way.
More than 200 people and eight helicopters were involved in the rescue operation.
Some of the injured were flown by helicopters to hospitals in Lausanne, Bern and other Swiss cities.
Swiss journalist Ruth Seeholzer told the BBC that the two-lane tunnel was not busy with traffic when the accident happened and driving conditions were normal.
The Belgian royal family has issued statements expressing deep shock at the tragedy.
Belgian Foreign Minister Didier Reynders said: "It is incomprehensible. There were three buses and only one was in an accident, without any contact with another vehicle."
A helpline for families has been set up, and many relatives are expected to arrive in Switzerland later.
Belgium has made two aircraft available to take them to the country.
Belgium's ambassador to Switzerland, Jan Luykx, has already travelled to the crash site.
He said: "This tragedy will hit the whole of Belgium. The magnitude of the accident is difficult to take in. For the moment I am concentrating on the practical aspects. The emotional side will come when we meet the families."
European Commission president Jose Manuel Barroso sent his "sincere condolences and deepest sympathy" to the victims' relatives.
The European Parliament was to observe a minute's silence at noon.
The head of the Valais region, Jacques Melly, also expressed his deep sadness at the accident and praised the rescuers for their work in "extremely difficult conditions".
