In August, the Ted actress was reported to be "having fun" dating Kutcher after the pair were spotted on vacation together.
A source has now told Star magazine that Kutcher took a "leap of faith and asked her to move in".
The pair are said to be "in love" and have decided to live together as they "spend so much time with each other".
The source went on to say that Kunis is planning on redecorating the home as Kutcher doesn't want her to "feel like she was living in a bachelor pad".
After dating for around two months, following Kutcher's split with wife Demi Moore last November, the pair are reportedly planning to adopt a dog together.