The decision opens the door for perhaps hundreds of other children around the country in a similar situation.
In a statement to the press, Malmö district court said that "it cannot be ruled out that there is an economic motive behind [Vellinge's] decision."
The court said that the decision to send the boys, who are now 23, to the school had not even been discussed with the parents.
The brothers were in class five when they were sent to the special needs school. They had dyslexia and needed extra help.
It is not yet known how much compensation will have to be paid. Vellinge council will also have to pay the brothers court costs.
Robin and Rasmus Sjöholm's lawyer, Magnus Dillcrona , was overjoyed with the result.
"I am so happy for the twins sake, and now it is just a question of how much money they receive."
It's not the first time that the council has courted controversy. In 2009, the conservative led council was widely condemned for its decision to refuse to accept housing for unaccompanied refugee children.