Betty's 3,029 square foot home in Brentwood, CA is listed for $10.575M. It has some great views of the famed Getty Museum ... with a massive backyard outfitted with the obligatory SoCal swimming pool.

Betty spent many years here -- she moved there in 1968. She lived there with husband Allen Ludden because it was central to a bunch of studios on the Westside of L.A. Betty stayed put after Allen died in 1981 ... in fact, she lived there until she died in the home last New Year's Eve.

There's also a guest house, where Betty and Allen enjoyed playing charades with friends like Jimmy and Gloria Stewart, Dinah Shore and Burt Reynolds.

If you're a lookie-loo, don't bother ... the only people who can tour the home are prequalified buyers and will be given no interior access to the home.

As we reported, a buyer has already laid claim to Betty's home in Carmel, CA, where Betty also spent lots of time. That house is incredible, with views of the famed Monterey Peninsula. It was listed at $7.9 mil, and a bidding war hiked the final price to $10.7 mil.

Betty wanted to live out her final days in the Carmel home, but had to live in the L.A. house for medical reasons.