Last week, former Olympian Bruce, 65, gave a two-hour interview to ABC News, where he confirmed ongoing rumours that he is transitioning into a woman.
Keeping Up With The Kardashians star Kim said on Jimmy Kimmel Live! yesterday: "Bruce is doing really well, he is so happy and I think it's a sense of relief from all of the amazing support that he's felt.
"It's a really brave thing to come out and be so truthful. And to have all of that support just meant the world to him, and our family."
Bruce had said during his two-hour interview that Kim had been very supportive, and that she told him he'll need to know how to dress well.
"Yes I said, 'The only thing is, whatever you do, do not steal my glam team, they are mine!'" said a laughing Kim to Jimmy.
"There's too many girls in this family!" she continued. "I did tell him that, whatever help you need, you need to look and feel your best. If you need any help with anything, style-wise, glam-wise, I'm here to help you."
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Watch Kim speak about Bruce below: