The actress offered up her home to the talk show host, but has a few complaints about her stay.
"The world knows our first guest from a little show called Friends, but currently I just know her as my landlord," DeGeneres quips while introducing the actress.
"I don't consider me a landlord," Cox disagrees. "I consider myself your roommate."
As for why DeGeneres, who's married to Portia de Rossi, left her own home, she jokes, "I'm not having marital troubles... I'm not living with Courteney Cox because I'm kicked out of my house."
"We sold our house here in Beverly Hills," DeGeneres says of herself and her wife of more than a decade. "I needed a place to stay and you were kind enough to say, 'Yes, stay at my house.'"
While Cox was happy to let DeGeneres move in, she hasn't been all that thrilled with her guest's actions.
"You're my style guru, so I was nervous about you staying there, being that I haven't redone it. I haven't been there in a year," Cox says. "I had it cleaned. I moved everything off of the right side of the bathroom, so you'd have your space in the drawers. I was just really ready for you."
When Cox's assistant stopped by the house, though, the actress wasn't pleased with what she saw.
"And all of the sudden it was like, 'Wait a minute. Ellen's toothbrush is on my side!' I had her open the drawer and I was like, 'Well, where's my makeup?'" Cox recalls. "So essentially you're a terrible roommate. You took over my side and your side."
"That was Portia who took over your side," DeGeneres replies. "I only have one side. She happened to be there one night."
DeGeneres assures Cox that her "makeup is still there, and it was just one toothbrush on that side," before sharing a few complaints of her own.
"Can you get that [piano] tuned?" she jokingly asks Cox. "And just move some of your stuff in the closet over, too."
Watch the video below for more on DeGeneres.