The apartment is located a few blocks from her family home on the Upper East side of Manhattan and also near the Kabbalah Centre.
The amount that the 54-year-old paid for the property is undisclosed but it is 'in a secure block with a lot of security and access to a swimming pool and gym'.
The expensive gift comes shortly after it was reported their relationship had become strained in recent months, with Lourdes rebelling against Madonna, and threatening to move in with her father Carlos Leon.
Lourdes turned 16 Oct 14.