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.
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