The couple, who moved in with the reality TV star's mother, Kris Jenner, shortly before the birth of their 18-month-old daughter North in June 2013, have splashed out $2.925 million to secure the property next door to their existing $20 mansion in Hidden Hills, California.
The deal for the rustic four-bedroom, three-bathroom house, which sits on 1.49 acres, closed on December 15, according to the Trulia.com.
A source told gossip website TMZ.com the duo are now planning to demolish the property so they can expand their original abode, which they have been renovating since buying it in August, across almost five acres and build a giant children's park.
They are also eager to build a basketball court and full recording studio for Kanye, 37, so he doesn't have to travel to Paris to record new music.
Their sprawling estate will also include a full cinema, game room, a detached guest-house and spa for Kim, 34.
The couple moved in with Kris, 59, in order to renovate an $11 million home in Bel Air.
But earlier this year they decided to put that property on the market and bought their Hidden Hills house, as they got fed up of waiting for the extensive work to be completed.
Kim recently revealed they are planning to move into the house this month, and a source close to the 'Keeping Up with the Kardashians' star said: "Kim can't wait to get into their new home.
"Living with Kris, her baby and husband wasn't the most ideal, but this will be their forever home. They can't wait for friends to stay with them!"