Östberg has been moved to the centre close to Södertälje, south of Stockholm, according to the newspaper Länstidningen.
She was first transferred to Hinseberg prison, near Örebro, from a Californian jail in the spring of 2009.
Having been convicted in 1983, Östberg spent 28 years imprisoned in the US for her role in two murders.
In October 2009 she was moved to Färingsö prison, a lower security facility.
Östberg has now been granted her request to be housed in the rehabilitation centre and work at a nursery for dogs before being released next year.
In November 2009, the district court in Örebro reduced her life sentence to 45 years, claiming there was no major risk she would revert to violent crime.
Under Swedish law, convicted criminals are eligible for release after serving two-thirds of their sentence. In Östberg's case, that corresponds with a release some time in May 2011.
Östberg moved to California with her mother in the 1960s. Having suffered from serious drug problems she later started a relationship with a drug dealer, Brian Cox.
In April 1981, Cox, accompanied by Östberg, shot dead two people in separate incidents.
Cox hanged himself in his cell prior to the trial, while Östberg was convicted and sentenced to life in prison for the murders.