If you are a non-EU resident moving to Sweden it is slightly more complicated to apply for the right to live and work in Sweden. You need to apply for permanent residency via Migrationsverket (the Swedish visa and civil registration agency). There are several criteria that you can meet to apply for permanent residency.
Moving to someone in Sweden (EU citizen or Swedish citizen).
You must be either married, registered partner or common-law spouse of someone already living in Sweden, lawfully or planning to marry someone already living in Sweden, lawfully. In this situation you can apply for a Permanent Residence Card. Here is a link to the application.
You can also move to Sweden to be with a close relative.
Children over the age of 18 or parents of an adult child with permanent residency. Again, the family member the person is moving to must have a permanent residency permit. Here is the link to applying for permanent residency for a child.