The law had been discussed for years, but was finally decided last autumn as part of a broader agreement on immigration between the government and the opposition.
"A few municipalities took a very large responsibility, while others did not, and that is unreasonable," labour market minister Ylva Johansson tells Swedish Television News.
How many refugees will be assigned to a municipality depends on its size, the labour market in the area and on how many refugees that have already moved there.
Among those municipalities that over the past few years have received very few refugees in relation to the population are Staffanstorp, Vallentuna, Vellinge, Lomma and Kungsbacka, news agency TT reportas. Now, 318 refugees will move to Kungsbacka and 159 to Vellinge.
In addition to the 21,700 refugees that are part of this process, some 34,000 refugees with residency permit have already organised accommodation on their own. There are over 20 municipalities where already so many refugees have moved, that they will not be required to accept any more as part of this programme during 2016. Södertälje and Östra Göinge are two such municipalities.
In addition to this, a separate programme is also underway that will divide up the unaccompanied minors among the municipalities.
The local councils will be reimbursed by the state for each refugee that they take on.
"Some of the compensation has increased now, and some municipalities say the money is sufficient, others say it isn't. The picture is not clear-cut," said Per-Arne Andersson at the organisation for the local and regional councils SKL. In addition to the challenge of finding housing for everybody, Andersson notes that several council also need to build several new schools to meet the demand.
According to TT, one third of all the asylum seekers are of school or high school age, and in the forecast from the Migration Agency, the increased need for schooling continued to be a big challenge for the municipalities.