The couple - who have children North, two, and Saint, three months - originally moved in with the showbiz matriarch three years ago while their Bel Air mansion was undergoing renovations, reported People magazine.
Moving trucks were spotted at the house earlier this week, and West has now confirmed the relocation on Twitter.
He posted alongside an image of a floral arrangement in the house: "feels good to be home (sic)"
The couple bought the property for USD 11 million in early 2013 and planned to add a gym, cinema, hair and make-up salon, bowling alley, basketball court and a number of swimming pools.
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