The 32-year-old reality star shared a Snapchat video of herself kissing the 25-year-old NBA star following brother-in-law Kanye West's show Friday in Miami.
Kardashian and Thompson were first linked in late August after being spotted at Bootsy Bellows in Los Angeles. The pair enjoyed a getaway to Cabo San Lucas, Mexico, over Labor Day weekend and were seen kissing at Drake's concert Sept. 9.
"[They] are seeing each other," a source told Us Weekly. "She seems more hopeful with Tristan -- he's different than the other guys she's dated. He's a committed, relationship guy."
Kardashian's mom, Kris Jenner, told news outlets she approves of the romance while attending the Brent Shapiro Foundation Summer Spectacular on Saturday. The 60-year-old reality star was accompanied by her boyfriend, Corey Gamble.
"[Tristan's] a wonderful guy. I've met him and he's great," she told Entertainment Tonight. "[Khloe] is a delicious girl. I just want her to be happy. She's having a good time."
"They are really cute," the mom of six added to E! News. "I think just with any relationship, just in life, I think it's about chemistry and about values. You know, about how two people get along."