Iggy Azalea's Keeping Up With Kardashians As Their New Neighbor

Iggy Azalea has moved into Kardashian country ... renting a new pad inside their gated community for around $15k a month.

We're told Iggy got the home 4 months ago in The Oaks -- where most of the Kardashians and Jenners live -- right after she broke off her engagement to Nick Young.

Sources close to Azalea tell us renting makes sense for her right now while she's looking to buy. Plus, she wanted to live near horse facilities because she's an avid equestrian.