Her father Daniel told ABC News the teen has had five open heart surgeries and has been in and out of hospitals for most of her life.
"My daughter lives a pop culture life because of her ailment," Daniel said. "She's not hanging out or going out on dates, so she spends a lot of time with the television."
As Meghan's condition has worsened, she has become terminally ill and, when she turned 18 in March, qualified for the Dream Foundation, an organization that grants wishes to terminally ill adults.
"I didn't think Taylor would be obtainable because she's the biggest star in the world," Daniel admitted.
Still, he took to Facebook in an effort to make Meghan's wish of talking to Taylor Swift come true. The post soon went viral and after several leads, Daniel got a text Thursday saying that Swift was set to video chat Meghan.
"Sure enough, Taylor called, and they chatted for a little close to a half an hour," Daniel said. "[Meghan] was truly starstruck. I was filling in some of the conversation because Meghan was like, 'This is crazy!' That's what she kept repeating."
"I don’t think she really believed that it could happen or would happen, and it did," her father added.
Meghan took to Twitter after the phone call to say thank you to her favorite singer.
"The words thank you will never be enough to say to Taylor Alison Swift for this day and taking the time to video chat with me for 19 mins on September 8th, 2016. Thank you from the bottom of my heart Taylor," she tweeted.
Daniel said his daughter has inspired him.
"I’m very proud of how positive she’s remained despite her life being so trying," he explained. "Much of her life, she's been hospitalized but she’s always wearing a smile and always very, very upbeat and everything. She’s inspired me as her father ... It’s quite a motivator."