Bruce Jenner -- Kris Can Have All 8 Bathrooms

Bruce Jenner may have snagged Kris Jenner's best friend ... but he's giving up something probably way more valuable.

Bruce signed documents -- obtained by TMZ -- giving up his share of their Hidden Hills house to Kris in their divorce property settlement.

They bought the 6 bedroom, 8 bathroom pad in 2010 for $4 million and it's gone way up in value.

Bruce is now ensconced in a bachelor pad in Malibu.

As we previously reported ... Bruce recently started hooking up with Kris' friend and neighbor, Ronda Kamihira.