TMZ first reported the purchase.
Mr West’s $4.5m home is across the street from Ms Kardashian’s in Los Angeles.
The couple have four children together. The proximity of the homes will presumably allow the celebrity parents easier parenting arrangements.
The five-bedroom home is just over 3,650 square feet, and cost Mr West $421,000 over the home’s asking price. It includes a swimming pool and a stable for horses.
The couple originally lived in Ms Kardashian’s house together, which Mr West designed over a number of years. After the couple split, Mr West have his interest in the home to Ms Kardashian.
This is one of several real estate transactions Mr West has made in recent months. In September, the celebrity musician purchased a $53.7m beach house in Malibu. He has also recently listed another one of his properties for $3.7m.